My sister is not married, has a son with boyfriend, can she move out?

[mistoffolees]

Pointing out that he is NOT the primary caretaker, does not automatically mean that she IS the primary caretaker. It could easily be an equal situation.

Yes it could. She could be the caretaker. So could he.

You said that he is NOT the primary caretaker but there's no evidence that this is the case. Without more information, you can't rule out the possibility that he is the primary caretaker as you tried to do.