But we don't know what ex status is or her kids and whether they have any upcoming interviews where they can be asked about living situation.
We don't know what all paper trace ex and her kids are leaving by residing at OP's husband house. And if he tries using this address at any point in process, it can be flagged. With great level of certainty fraud department at USCIS incorporates AI to some degree, allowing searching and analyzing thousands of cases and any matching data - addresses, names, birth etc etc.
At the end of the day, USCIS has ability to see sealed / expunged charges, involve FBI in background checks and many more. I wouldn't underestimate their capability to gather information.
Any person's phone (OP, husband) can be searched by CBP too - checking any messages when entering the US.
I wouldn't leave any chance for this to screw up OP's immigration.