It’s a fairly normal situation for divorced fathers to pay for the housing of their children. I agree the ex living there is a bit odd, but given the context of the relationship (he owns a house and lives overseas; no reason to pay multiple housing payments in the U.S.) I don’t think it’s that out of the ordinary and is something I’ve seen within the US when one parent moves states and the kids and ex don’t.
It would be a huge red flag if he was living with the ex, but she has custody and he’s supporting the children. It might even be within the terms of the custody agreement.
These are all things we don’t know, and more to point, the government doesn’t know or have any real way of finding out without disclosure. Yes they can send agents, but in a consular case with both parties living overseas that’s extraordinarily unlikely; even more so than the already low odds of it for AOS. Discussing the unlikely worst case isn’t that helpful.
There’s no proactive disclosure requirement on this, and it’s bad advice to tell someone to change their entire financial relationship for the upkeep and care of their children because a theoretical issue with the government in the future. They should be prepared to address the issue if it comes up with a good explanation (custody agreement, etc.) and it might make sense overall to change their entire financial arrangement with the ex-spouse, but I wouldn’t let immigration be the driving factor.