I can only offer:
Right now you have dual citizenship. If you wished, you could move to the USA. You say you have no plans to do so, but heaven only knows what the future may bring. You've already lost the option of moving elsewhere in the EU because of Brexit. Conditions in the UK could deteriorate substantially (in a worst case) and you might be better off bringing your family to the US to live than remaining there. You won't have that option if you renounce. So I guess my suggestion is to weigh the relatively minor hassle of reporting to the IRS every year (and it should be minor, now that you've sorted out all the "back taxes" issues and is something you can do yourself without a hired consultant) v. not having an option to "jump ship" to the USA if things do take a turn for the worse there in a substantial way. You would be burning not only your bridges, but a potential economic safety net if you renounce.
Your children - as I understand it they are not US citizens because you did not spend the requisite number of years in the USA and are married to a UK citizen. If that's incorrect, and if they were eligible for US citizenship, I would want to see that they had it. It gives them the "wiggle room" to move to the USA if things don't go well for them economically (or otherwise) in the UK. And it would give them the option to make the decision for themselves re: dual citizenship. I had a parent make a decision about my own dual citizenship (not UK) without even alerting me they'd done so. While I was able to get around that as an adult, it impacted my own child and deprived her of that option. She and I are still pretty ticked off with my father about that. (Of course, if your children are not automatically dual citizens, it's a moot point.)
[I would imagine you'd already considered all of the above, but just in case not.] I'll leave all your other questions to people who will have the information I can't provide. Best of luck, whichever way you decide to land.