Well, MN doesn't work like that. 
of course you are able to go on holiday outside of term time, that's right and fair. I assume their mother ALSO takes them away on holiday?
You DO have to understand that your decision to take the kids out of their education to this extent isn't right. You are undermining their schooling.
Perhaps if you re-thought the schooling? send them to a Jewish school? or better a private school, it wouldn't impact them so much? You have to put the kids first. the situation you describe doesn't seem to suggest this.
By the sounds of it, you are tacking on "family" holidays to a religious reason, knowing that it can't be refused, and this is why their mother is (potentially rightfully) pissed off. Do you have kids of your own? are they also missing school?
perhaps their mother thinks you are playing families with her kids?
That said, if she is being malicious, there are ways she can be encouraged to stop, police, lawyers etc.
Of course she could be crazy and you may be utterly blameless, but if you are as abrasive with her as you are with us, and if the situation is new, and one over which she has zero control, it may explain why she is doing anything and everything she can to get her kids education sorted out better, it may explain why she is so pissed off.
Have you thought about asking the Rabbi for guidance to mediate and negotiate this?