I would definitely try to keep it local if she does end up filing. My
DH's ex changed the jurisdiction with his agreement (he is military--was in the same place for 6 years and then we got stationed overseas and
BM was out of the state he was in). My DH had court papers filed by BM 3 months after the one Court hearing because it was cheaper and easier for her to file, given it's right there with her.
And I agree with keeping the child there with you all during his parenting time, even if she throws a fit about it. Once he stops giving in, sure she'll raise hell for a bit, but eventually she will get it that he's not giving in.
I hope everything works out for you guys!