So with her being so volatile, this doesn't seem like a situation where you want to make a major decision like moving, based on her whims. Isn't she living with her mother? That doesn't sound like a lasting situation.
You should have the kids with you more, at their home. She is the one who took the children and left. If that was not due to abuse, you should go after getting the time with them that is fair to you and them.
I believe I've asked this before, but never saw an answer - but why are you going along with her decisions on this? Is she holding something over your head?
Where do they go to school? Has she changed their address? If she has, you can go and tell the school it was not with your permission, and get it changed back.
Did you talk to an attorney? It sounds like you need to do that very quickly, if you haven't already.
And yes, she has lost her marbles for now. Don't expect her to be rational and logical, and don't get upset that she's not.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17