Self-Guided Driving Tour of England, Ireland, Scotland - Need Help Planning!!

Oh gosh, your thoughts unfortunately are totally beyond all possibility. You are going to have to take a chainsaw to what you were thinking to attempt. With only 2 weeks I would suggest you look for satisfaction with just London and a little bit of England and Scotland.
So yes, forget Ireland and Paris.
Oh, and you will be best without a car for most of your time.

Day
1. Arrive Heathrow. Pick up car. Drive to Oxford (2N)
2. Day to Stratford-on-Avon
3. Drive via Cotswolds to Bath (1N)
4. Drive via Stonehenge to Salisbury (1N)
5. Drive via Highclere Castle to Windsor (1N)
6. Return car at Heathrow. Fly to Edinburgh (3N)
7. Edinburgh
8. Edinburgh
9. Train to York (2N)
10. York
11. Train to London (4N)
12. London
13. London
14. London
15. Depart Heathrow

Have you considered flying over to Ireland and back over to Scotland? Budget airlines are the secret to efficient and inexpensive travel instead of ferries.
I'm amazed how good some of the large travel consolidators' fly and drive trips are--and very, very inexpensive in places like Ireland and/or Scotland. See Tripmasters.com.

My plan is to spend 2 days in London, seeing all of the typical central London sites ( Tower of London, Big Ben, The Eye, Westminster Abbey, Windsor Castle, etc)

I can't see that happening unless you want to just drive by and check a box, "Been There". Windsor Castle alone will take most of a day, parking is very expensive and like hen's teeth in Windsor. If you took the easy, fast and frequent train right there you could stay as long as you like with NO hassle.

Have you ever driven in the UK? If not, add 50% to the times you think it will take to reach places and get parked.

Most parking in the UK is at "Pay and Display" lots where you have to guess how long you will be and pay for it at the beginning. There are many fewer "Pay on Foot" lots where you get a ticket and pay for what you used when you return to your car.

use a LondonPass and Travelcard to avoid parking and traffic

How does that work? In order to have a rental car while you are in London you will have to park it while you are using your London Pass and Travelcard. Have you figured out where that will be and how much it will cost to park that not going anywhere car?

The third day we plan to drive out to Stratford Upon Avon to visit Shakespeare's birthplace

Be careful - parking in Stratford upon Avon is tricky. They have a whole herd of uniformed parking officials who hand out bucketloads of fines every day. I know. I used to live just down the street, and was there last week. It has become even harder.

There are trains which take you right into Stratford and the town is very walkable.

Many rental cars are not allowed on ferries.

The last day we plan to take the ferry over to Paris for a quick visit to the Eiffel Tower and a meal, then back that night to prepare for flying out the next morning.

90 minutes to drive to the port from London, check in for a ferry a minimum 90 minutes in advance, 90 minutes crossing, 30 minutes to disembark, 3 hour drive from Calais to Paris if you have zero traffic and don't stop, and driving in Paris and parking there make London look like Podunk. So 8 hours each way = 16 hours round trip for a drive-by? The Eurostar train does it in 2:15 each way with a 45 minute check in.

Your car, with no traffic and no roundabouts and no stopping can do 70 mph except where it can't. Trains in the UK do up to 125 mph with onboard toilets and food, no roundabouts and no traffic, centre to centre. No contest.

You can be spontaneous using the train. too, you know? All the places you listed are easy by train. You can even use a train for crossing the Irish Sea with Rail'n'Sea.

As your plan is now you will need time turners and need to know how to use them. It isn't practical.

My first thought was that this was a spoof post as the itinerary is so far from being realistic, that I thought it was a wind up!

Hire a car after you have seen London - allow a day for jet lag if needed and add another night to London - there is plenty to keep you occupied for 2 full days plus Windsor is another day.

Stratford upon Avon can also be covered from London by train, so add a 4th night to London. SuA was a huge disappointment for me - far too much of a tourist trap. Driving here from London is likely to take 3/3.5 hours. Parking is a nightmare.

SuA to Stonehenge - say 2.5 hours driving. Visit Stonehenge - 3 hours to view. Drive back to London - c 2.5 hours +. That's a 13.5 hour day, allowing only 2 hours in SuA. That's 5 hours of sightseeing and 8.5 hours of driving. No time for a show that night.

Drive to Liverpool - allow 5 hours minimum. You will pass fairly close to SuA. Liverpool to Holyhead - say 2.5 hours. The crossing is 2-3.5 hours. Travel time 9.5 hours. Doesn't leave much of the day for seeing Liverpool.

Most car hire companies do not permit you to take their car to Ireland. Your Scottish element is just as flawed. Inverness to the Orkneys is more travelling than visiting - best from John o'Groats. Skye is best with 3 days as it takes time to get around on the narrow roads - most accommodation is booked here up to a year in advance, so you may struggle to find somewhere.

Sorry, but your plan needs a major rethink. You need to work out your priorities. You don't have time for Paris if you include Scotland and Ireland.

Book into London and home from Ireland or vice versa. Have 3/4 days driving in Ireland. Fly to Edinburgh or Glasgow and hire a car for a few days driving in Scotland. Take the train to London - 5/6 nights including a day in Windsor and another in SuA or Stonehenge. Paris deserves longer than a few hours, so leave this for another trip.

My recommendation is to go west to east to south. This itinerary is not relaxing, but I get the sense that you're go, go, go, kinda people. :) Adjust as needed. I have listed nights here so that it's clear you're sleeping two nights in one place, etc.

Night 1 and 2 - Fly to Shannon, rent car, (get every insurance option possible - credit card insurance doesn't cover ireland). See Cliffs of Moher on arrival day, drive to Dingle, stay in Dingle (2 nights). Day in between can be for enjoying Dingle Peninsula. I'd give up on Ring of Kerry for this trip.

Night 3 and 4 - Traverse Ireland via car to Dublin. visit sites in Dublin (2 nights). One full day in Dublin. Honestly, I'd go to some pubs to hear trad Irish music and order a Guinness and forgo the Guinness tour. But that's just me.

Night 5 and 6 - Drive north to Belfast - do you want to do anything in Belfast? Political Taxi tour is really interesting. If not, keep driving and stay in town on Antrim coast two nights. Portrush is nice, Derry is great (walk the ancient town walls). Stay 2 nights so that you have a full day to do the Antrim coast sites (if that interests you) - Giant's Causeway first -- early - before crowds, Dunluce castle, Carrick-a-Rede bridge, and Bushmills distillery. All in a day is easy. Have done it twice now.
Drive back to Belfast (unless you're in Derry and there's a good flight), drop off car, and fly to Edinburgh.

Night 7 - Rent car in Edinburgh. Do you want to see Edinburgh? The Royal mile and the castle are interesting. Especially if you get there in the late afternoon the castle isn't too crowded. Do the castle first, walk down the royal mile, and stay in Edinburgh one night.

Night 8 and 9 - Drive north to Stirling and Glencoe for haunting views of Scottish highlands. You can feel the history in the hills up there. Stay a few nights in the highlands so that you have one full day. Do you like Harry Potter? You can go up to Loch Shiel (just north of Glencoe) and take a relaxing ride on boat in Loch Shiel and be there when the train goes by. There's a microbrewery there, too. Can get lunch. Makes for a nice day.

--I recommend forgoing Isle of Skye unless you want to add another 3 days to your trip. It's not a day trip kind of place. In addition, Loch Ness is one of hundreds of lochs you will see as you drive around Scotland. I can understand the interest, but I'd not make it a destination.

Night 10 and 11 - Drive south to England. I've been to the Lake District and not to York, so I'll leave that part to you. Plan on two nights in northern part of England so that you have a full day in York.

Drive south to London. (You are missing a lot of beauty by just going directly to London, though, but with two weeks you have to be efficient.)

Night 12, 13 and 14 -- Arrive in London, drop off car, and spend three nights somewhere very central. This gives you two days to see the most important sites that you want to see.

No Paris on this trip, which seems a shame. Find 3 days to shave off of this itinerary and gift yourself with two nights in the City of Light at the end (and then fly home from Paris.)

Enjoy!

EXCELLENT feedback, thanks so much, everyone!

Particularly helpful info, Wendy and Nigel - thank you! We are definitely on the go people, and plan to use every minute possible of the two weeks. If my daughter had more vacation time we would stay longer :( But, at least we will know the things we want to do on the NEXT trip. I also contacted a friend who is in Edinburgh, and we definitely want to stop in for a pint with him while on our way through. He also had a great bit of info for us, so we are much more confident in the itinerary now. FYI - Irish Ferries and the Stena Lines do indeed allow rental cars on the ferries. The hitch is that the rental car company needs to approve of the vehicle leaving the country - which was an obstacle, but has been resolved by changing rental companies.
Again, thanks for all of the input, I truly appreciate the help!