So I have to say that I stand by the motto "You reap what you sow."
The ex-spouses have been divorced since 2015. The ex-wife knew what was coming and that by the end of January 2021 a financing/solution had to be in place if she wanted to keep the house. The ex-spouses are divorced and since the relationship between them is unfortunately not great - for whatever reason - the ex-husband naturally does not want to continue "guaranteeing" with his name. Both the ex-wife and her new husband, with whom she has also been in a relationship since 2015, knew what was coming. If the new spouse is then studying in the x-th semester, failing exams, has a child born in mid-2019, and at the end of his 30s does not generate a fixed income and they can only afford this standard of living because of the child support from the ex-husband, then you have to live with the consequences. In my opinion, the spouses have to be able to manage it together. You can neither expect concessions from the ex-partner nor from the (in-law) parents to make themselves available as guarantors. If you (still) cannot manage it on your own strength, then maybe just a little later.
In any case, I thank everyone here who has engaged with the topic for their opinion.
At the end of the month, it will then be seen whether the core question "will child support and child benefit be taken into account in the financing?" could be clarified.