The father is way out of line.

If he really wanted help because his new family needed it so badly, that would have required a conversation, reconciliation, and agreement to move forward differently.

Not a demand to pick up his child from school.

The author is right to stand her ground here.

And that poor kiddo? Maybe there are better ways to offer her help - if you are so moved - on your own terms - because you want to help. Not out of manipulation. And maybe there aren’t good way.s? Sounds tough! Good luck.