Because of her financial situation, moving her in as an additional sex partner can create a really icky dynamic. I am not saying this to suggest it a sex for a roof situation but sometimes people feel that way, feel others might be seeing them that way, more likely to act out poorly. Has this been addressed by everyone? And since this is getting considered a triad maybe trying talking to the both of them about what's on your mind at the same time before trying to do it one on one. It can help keep things above board and make it harder for anyone to make false accusations about happens or gets said.
Is there room for you to find a partner while they enjoy their connection if it does become a no go for a triad? Is it possible for her to just be a roommate and not a sex partner to you or your SO?