Azoi: I’ve come up with a potential brainstorm solution for your dilemma. Tell your daughter to ask your non-blood relative that she is married to for a divorce. This way she can buy the house post-divorce, insuring he has no interest in it. After all, even if it is in her name only, as long as she is married to this non-blood relative guy that you don’t want his name on the deed, it is always possible divorce court will grant him a partial or full interest in the home, since it was purchased during their marriage.
The only possible glitch is, that since halachicly your daughter is not entitled to a ‘get’ just because she wants one (there is no divorce-on-demand in Judaism), he may justifiably refuse to give her a divorce under halacha, and he would be within his full halachic rights to do so.