The bulletproof part is that the kids stay. She is not to move the kids out of the MH, that is the bulletproof part. She does not have sole custody (she may well go for sole custody). Have the lawyer draft a legal notice that she is not allowed to remove the kids from MH without your consent.
Just what exactly are you confused about?
With regards to the kids' "blackmail" you have to nip that one in the bud and remove any and all hints that they have a say with regards to where they will stay.
