I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear that this is happening.
She's allowed to stay home and not work if her new spouse is willing to support her, however, for child support purposes, the judge should assume that her income has not changed. The calculation should be done assuming that she makes as much as she would be if working full-time. Then, she's till partially responsible for contributing to the children's support. Take a look at this calculator to see what he should be paying. If the most recent order is not in-line with that amount, he can file a Motion for Reconsideration.
If he's going back to court, anyway, he can ask the judge to order the mother not to disparage the father around the children or let other people to do so, to make efforts to repair that relationship, and not present stepparent adoption as an option. That might help a little, but he could also consider whether he wants to tell her to stop texting him at all, or even block texts from her number. Or he could ask the judge to order that they go to family therapy to try to resolve things.
You should know that if he signs over rights to the mother's husband, the mother's husband when then assume his child support obligation, and he would no longer have to pay anything. But it's understandable if that's not what he wants to do.
If you have any questions or concerns about my response, please reply WITHOUT RATING. It's important that you are 100% satisfied with my courtesy and professionalism. Otherwise, please rate my service positively so I am paid for the time I spend answering questions. If you are on a mobile device, you may need to scroll to the right. There is no charge for follow-up questions. Thank you.