Definitely sounds like she's trying to get into primary status with him.
Before C moved in with M and me, he often felt like a "third"...or M's secondary. It was only when he moved in with us that he felt more like an equal part of the triad.
Currently with the three of you each having your own place, it's pretty equal. But your guy moving in with her, but leaving you still on your own, could skew things in her favor I'm afraid.