We'll only be in the UK for 2 weeks at a time whenever we visit.
A good to know.
Just be careful, because if you are stamped in as a visitor, your ILR could become invalid and then if you wanted to move back to the UK, you would have to start all over again with a spousal visa.
If you're planning to stay in the UK for the full 5 years, I would strongly advise to apply for citizenship as soon as you can.
It's 5 years to ILR and then you can apply for citizenship immediately after you get ILR. If you do that, you won't have to worry about visas ever again - you can leave the UK as often as you like, you can live in the UK at any time you want for the rest of your life and you can live and work in any EU country (as long as the UK stays in the EU).
I don't think I'll relinquish my US citizen for a UK unless we're dead certain that we want to retire to the UK.
No need to relinquish your US citizenship at all - you can become a UK citizen without losing your US citizenship... you just end up holding dual citizenship.
The only thing is that the US 'does not recognise' dual citizenship, which means that to them you are a US citizen and a US citizen only - they will pretend that your UK citizenship does not exist... which just means you can only enter and leave the US on your US passport, because as a US citizen, it's illegal to enter the US on a foreign passport.
The only way to lose your US citizenship is if you formally renounce it in front of a US government official... and it now costs $2,350 to do it (it just increased from $450)!