What do you actually want?
You mention if you moved out you prob wouldn’t move back in which to me sounds like you have had enough of the relationship. If thats the case, and thats fine by the way, you have two options depending on if you want to have a flat or live in the house with the kids.
1. Take the oppurtunity and leave.
2. Tell her if she want the space you’re more than happy for her to have it but your not willing to walk out on the kids, ergo she can have her space when she moves out.
If you actually want to make things work then I would suggest either option two or if she only wants a short space of time on her own then take the kids away on holiday for a fortnight. You get quality time with the kids, she gets her space. no one has to move out.
Good luck in whatever you decide fella