We do not have this problem...but, from what I have read, if your parenting order calls for right of first refusal - meaning the ex gets first choice of keeping the children whenever YOU cannot - yes, she can take the children. If not, she shouldnt be coming over. The police - that's a toss up, I would think..with or without an order giving her first refusal. But, maybe someone that has actually experienced this can give you better knowledge.
It may not be possible for you to have the same parenting time as you do now if the ex moves. That is when you get in and file papers as soon as you find out to modify the visitation orders to something that is possible...more summer time, holiday time, etc...