Is this a crazy idea

Sure, get a map out and mark your route. This is a necessary part to planning.

Usually when someone posts with a subject header like this the answer is "yes". But if you have lots of time and don't mind doubling back it could be fine. You would really hve to provide more details for anyone to say. I would not expect to rent a car and cross to Ireland on a ferry from Cornwall, as you would incur huge drop fees. You would probably have to double back to London to get to Ireland. Or better, double back to London and then Scotland, then to Ireland. You will be skipping over lots of places in between that have a lot of merit though. Sure you could do an itierary like this, but whether it's efficient and advaisable, not so sure. Whatever you do, make sure and fly open jaw and don't fly into and out of London just because the flight is cheaper, unless time is no issue and it's way cheaper.

Check out flights if you want to cover this sort of distance. You can fly London to Newquay in Cornwall, I'm not sure about on to Ireland but there are other destinations in tne Nirth of England you could fly onto such as Leeds.

You do not state your timespan. You can forget about the idea of taking a rental car across the Irish Sea.

Yes, it can be done, with time. I presume this is a 3+week trip?

Fly into Dublin for a week (presumably you want to be in southern not Northern Ireland?) and hire a car. Return the car and fly to Newquay for at least 5 nights or a week, where you would hire a car. Fly from Newquay to London for at least 5 nights or take the slower train, before then flying to Glasgow where you could spend another week with a car to explore the Highlands. Fly home from Edinburgh.

It would be a rushed trip if you only had 12 nights on the ground.

Of course! This is completely doable. I might suggest looking at rome2rio.com for ideas of all the transportation options between the places you want to visit. It shows all the possible ways from anywhere, to anywhere.

I’d probably suggest you do Ireland in a separate trip, otherwise plan to put it first or last and fly open jaw in to Dublin as suggested upthread and out of...Scotland or London or vice versa.

If time and finances allow, Scotland should be among your plans - rugged? Yes! The Isle of Skye has some civilized parts, and still-standing structures that were already ancient when King Arthur would’ve been just a prince, but also places that set the standard for ruggedness, like The Quairaing on the Trotternish Peninsula. Farther north, the islands of Orkney, and farther yet, Shetland, will offer both of you what you seek. Cheap Flybe airlines flights will get you there, and let the craziness turn into sanity.

The more that you plan for your trip, the more you will understand the mechanics of how feasible the trip will be within the TIME you have for the trip.

We started planning for our 4 week self drive tour of Great Britain. We planned to visit Wales, England and Scotland.
I particularly wanted to go to the village in SW Wales where my surname ancestors departed from for America in 1716.
The more that I researched the places that we wanted to visit and planned the travel, I realized that we didn't have time to visit Scotland during that four weeks. Yes, we could have done Scotland as well, but your visit to Wales and England would have been reduced in scope. We did our trip of Wales and England and it was great.

Here is my trip report with details.
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139