After reading your other responses in this thread it sounds like your culture is vastly different from mine.
The fact that you mention providing alternate housing for an ex, that would be her own responsibility where I’m from, and the fact that you decided to still live together while seeing others are plain weird to me.
I’d say a first step would be to have them meet each other with you there and then having brunch or something on their own. If either can’t stand the other then it’s not gonna work after all.