There were a lot of "should/will" sentences in all the previous explanations before the quote. How exactly is that?
Can ownership rights in the land register not be transferred directly, without the financing?
Without knowing for sure, I could imagine that it’s easier and faster to get out of the loan agreement if you’re no longer the owner.
On the other hand, it’s a zero-sum game since the loan installment and maintenance payments are offset against each other: if the loan disappears, the maintenance increases. So you could also continue paying the loan. It only becomes difficult when the first child no longer receives maintenance.
If all else fails, the only thing left is confrontation and tough measures: lawyers and partition auction. Depending on the mood of all parties involved, this announcement either helps or the atmosphere completely sours. Personally, I wouldn’t just let it run unresolved.
Addendum: What are the properties worth, that is the detached house and the multi-family house?
I think it would not be smart to transfer your ownership share in the land register but still remain liable for the loan. With the ex-wife, there is nothing to gain anyway; in case of doubt, the bank would turn to the ex-husband.
The bank will not release the ex-husband from the loan and leave the ex-wife alone in it, since she apparently is not creditworthy.
Taking out a loan for a house and bearing this "burden" for the ex-wife and her new partner is not particularly attractive. You are guaranteeing with your name.
A partition auction also does not seem to be that simple. The ex-wife might possibly avert it due to the "child’s welfare."
I am not aware of any market value.