Nine Days in only Ireland or Ireland and Scotland? HELP?!?!

The title of your post is misleading. You've already rejected the answer most people here will give you. You don't want to to just see Dublin or even more of Ireland, you want advice on how to do both Ireland and Scotland. Problem is that with such a short time you can't do any justice to either of them, and will possibly end up disappointed with both. My answer would be pick one or the other.

I don't have any answers on how you can do both efficiently in such a short time, but I hope someone here will be able to help you.

If this is really your only opportunity to visit Scotland and if visiting Scotland is more important to you than Ireland, go to Scotland.

However,

We just don't travel that much ($!)

.You need to do the math and see if the expense of getting to and from Scotland for your family is doable.

You'll waste most of a day switching hotels and travelling, so your 7 days is now 6 for seeing the sites. Only you can decide your priorities and if you think that's enough time for both. But my opinion is no.

If you decide to rent a car and take a ferry, check your rental terms, some don't allow the vehicle to be taken on ferries.

It's your trip so you get to make the choices, but some choices are better - smarter (based on experience) - than others. And you did ask for others' opinions, so people here will offer theirs.

Ireland - and Scotland - are bigger than most people think they are. Both are wonderful destinations. Each deserves some time - far more time than you can give them.

You have about a week of usable time on the ground in Europe. That's a very, very short trip, but you have to do the best you can with what you have. It seems to me that trying to split a week between the two countries would be a mistake. You will use way too much of your limited time just getting from place to place.

Stay in Ireland and do Scotland on another trip.

Just because you're flying to Dublin doesn't mean you need to spend any time in Ireland. Go to Scotland. Get there by whatever means makes the most sense (and, given your comment, costs the least) for your family. It's probably flying. Just make sure you have enough time between your flights to allow for delays, etc. Assuming you arrive at DUB in the morning, one option might be to leave your luggage at the airport and take the bus (I think the regular city bus, which is slow and "scenic," is the cheapest) into the city center and just walk around (Trinity College, St. Stephen's Green, Grafton Street, Temple Bar, the Post Office and back to Custom House/Connolly Station area--there, I made you a loop). Or do one of Rick's walking tours, which are free to download. Get some lunch and a pint, and head back to the airport for an evening flight to Edinburgh. Before you buy plane tickets to Edinburgh, make sure you can get accommodation. August is the busiest month in Edinburgh, what with the Festival, Fringe, the Tattoo, plus it just being August. A better choice might be to stay in Glasgow (or wherever, maybe where your family is from?) and do a day trip to Edinburgh.

Before deciding on Scotland— be sure to check out what hotel prices in August will be because you may be shocked at how high they are. In Edinburgh, $450
per night for just 2 guests is the norm at this late date. August is an extremely popular time and rates can be stratospheric.

If all you have time to see is Dublin and Edinburgh, then you're not really experiencing much of either Ireland or Scotland. They are both large, cosmopolitan cities, and most of the beauty of these countries is outside of cities.

It's not clear whether you want to travel around Scotland, or just visit some ancestral town. If the former no, if the latter yes.
You should be able to get a flight from Dublin to Glasgow or Edinburgh for next to nothing. Get an early flight and you can then travel onward by whatever mode to almost anywhere else in Scotland the same day.
In that timeframe ferry makes no obvious sense. Even if it did you would bus or train to Belfast, then bus via the ferry to Scotland, not self drive in a car from Ireland. You can or could rent at Cairnryan.
It all depends how important it is to you, your own priorities.
Anyone can give you a list of "must visits" in Ireland or Scotland for a week or two or longer. But the only thing that mat is your must do list.

A personal example - I have ancestry in Upper NY state, and New Jersey. I know perfectly well what the tourist must do's are in New York and how to spend a week there.
But if I flew in tomorrow for a week I'm going straight to a tiny town beyond Poughkeepsie for several days. Then a day at a nowhere town in NJ.
After that my absolute priorities in NY city are the site of a long gone historic hotel in the Bronx, the Cathedral of St John the Divine and a former newspaper office, now a shop.
They all matter to me hugely and my story, but would be irrelevant to 99.99% of English visitors.
Then, and only then, would I become a tourist for whatever time was left.

You say you got incredibly priced airfare. Does this mean your flights are already set in and out of Dublin? If this is the case, then stay in Ireland because you will waste far too much time getting to Scotland and back again for your flight home.

Ok here goes. We did that trip several years ago and it was a whirlwind trip but is very possible. Family wanted to do as much as possible in as little time as possible so we flew into Dublin spent that half day and the next three full days there then an early flight by Easyjet to Edinburgh for a half day then two full days there then early morning flight back to Dublin half day there and home the next. we had to fly that way as we were flying standby or we would have just gone to Dublin then Edinburgh and home from Edinburgh.So yes it can be done. Flying between countries is the most.efficient way to save time.be sure to get the ETA for use in. Scotland . Just be sure you work on sightseeing plans for on the ground to be super efficient on that part. Good luck.