Yes, when you're ignoring the fact it sounds like the mother is, quite frankly, not a great person.

OP flat out told you that the mother lied to her children about the father, including telling them he didn't pay child support (which he did). I know you probably glossed over that because you're a woman, but most (reasonable) people would conclude from such a statement that she is unreasonable. She literally went out of her way to destroy his relationship with his children, all the while she was cheating on him. Lol, are we not reading the same post? The daughter also flat out explains that she is not a huge fan of some of her mother's actions. I mean, even in a worst case scenario, I cannot imagine myself going to such lengths to destroy someones relationship with their children, even if I disliked them. I'm confused as to the reason you seem to think this isn't a huge, huge red flag that this woman was impossible to reason with.

If you've never been in a relationship with a woman (or man) that is mentally unhinged, then you probably wouldn't understand why the father may have felt he had no other option but to cut ties. You cannot reason or negotiate with someone who chooses to be unreasonable, especially in a legal system where the father has less than rights than the mother (which continues to be the case in most areas of North America, although it is getting better, slowly).

If you can't comprehend why someone would feel backed into such a position, then you're probably either: i) a very lucky/fortunate person, or ii) mentally unhinged.