Assalamu Alaikum
ekhi, it's not us, this is the way of the deen. You either follow it, or you don't.
Staying with a nonmuslim husband promotes more fitnah. Think about it.
If a woman has to obey her husband and her husband is nonMuslim, what would happen if he asked her to cook pork? came home drunk? if he gambles? wants to have haram intercourse?? What if he doesn't want her to wear hijaab because he doesn't think it looks attractive, or doesn't allow her to pray cuz he'd rather her do something else? What about the kids? Should they be raised Islamically or the way of their father?
These are just a few of the problems that could occur.
We are different from the kaffirs and our way of life through Islam is supposed to portray that, even if we do have some things in common.
If her husband isn't Muslim, how's that going to help her islamically with her faith? They might love each other, yea I get that, but just as Allah says:
fi aman Allah
w'salaam
This is true in some circumstances... but a husband and wife, that are full of love and respect, will not do something of the sort. He will not ask her to do something that is against her belief and way of life, that is wrong of him. That's like saying "Don't let the christian come to the masjid to learn islam, cause he/she might walk in with shoes, or the woman wont wear the hijab" when in turn christians do come to learn and out of respect they take the necessary actions they need to take to be respectible.
As far as proof goes, I haven't had the time to study it fully, so I can't really tell her what to do or not to do, and i'm just being down to earth and looking at the situation here.
Kidman