Is it permissible for a Muslim to encourage ones kafir mother to marry some other kafir?

Imagine this situation:

A Muslim lives with his kafir mother and her kafir partner (not his real father) in an apartment. The Muslim wants to marry a Muslim girl and life with her (at least for some year or so) in this apartment. In order to avoid the problem with the Muslim wife staying alone at home with the non-mahram partner of the kafir mother, the Muslim suggests that the kafir mother and her partner marry in order that the Muslim wife can stay at home in halal way. Because if she stays at home while alone with a non-mahram this would not be permitted I guess.

So could the kafir partner be turned into a mahram through marriage with kafir mother?

According to Beheshti Zewar Islam accepts other marriage forms (e.g. christian marriage) as valid. I do NOT mean that Muslim woman with Christian man marriage is valid, I mean that the marriage forms found in other cultures are accepted as valid marriage between kafirs by Islam. Therefore I guess the Muslim could make it possible for his wife to live with kafir mother/partner inside same apartment in a permissible way.

Is this correct?