What is there to prove? Two opposite sex people living together is the definition is of COHABITATION.
I am not the one with the burden of proof here btw. Regardless of whether it is cohabitation or not, since you two are of the opposite sex, what you are doing is a SIN because you are putting yourself in near occasion of sin.
The burden of proof is on you to show me why you have no choice. But nothing you have said so far proves that you don’t have a choice.
She has a place to live. She is not getting kicked out.
Her family might think Catholicism is satanic but that’s irrelevant since her faith is within her. What you are proposing is that she come and do something immoral which is to commit a sin and hence an immoral act. She has decided to become a Catholic while LIVING with her family. If she can do that much, she can certainly keep her faith and tell her family to respect her choice.
So as far as I can see, you have no justifiable reason to make what you are doing a necessity. She has ample amounts of choice, leading to tough times, but MORAL choices.
Choosing you might be the easiest choice but its immoral. Hence as a Catholic, it is not an option.
For the sake of her salvation (ironically, which is the reasons why you are saying she needs to move in with you), you have to keep her from sinning. Living with her family and going through a tough time IS NOT A SIN. But to move in with you and live with you IS A SIN because she puts her-self in near occasion of sin and possibly also commits the sin of scandal. So why can’t you see that you are not even doing whats best for her salvation?
God Bless