Sorry to hear that you're not feeling happy
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To answer your question about being able to stay in the UK, as you have ILR, your immigration status is independent of your relationship, so you can stay forever even if your relationship ends.
But ig you move back to the US, your ILR will only remain valid for 2 years after leaving... so if you do move back to the UK, you will have to do it within 2 years.
If more than 2 years has passed, your ILR will lapse and you will have to start from scratch with the entire visa process all over again... and if you are no longer in a relationship with a UK citizen, you would have to get a work or a student visa to be able to live in the UK again.
It would be a good idea to get UK citizenship before you make a decision on leaving - that way you will be able to move back to the UK whenever you like in the future and not have to worry about your ILR lapsing or qualifying for any visas. You would also have the right to live and work in any EU country as well.