Smart choice. Even if your husband did not have sex with her, it would cause massive tension.

Carol would be making unwanted advances on your husband. He'd be torn with with not wanting to throw her out after you invited her to stay and wanting to have sex with a hot chick who is throwing herself at him. He'd feel guilty about those natural physical feelings and be pissed at you for putting him in the situation.

He'd have to tell Carol to stop hitting on him. Carol would play stupid and say he's imagining things so that he wouldn't throw her out.

There are of course myriad ways it could play out, but the bottom in is that you inviting her to stay would end up putting a wedge between you and your husband, which is exactly what Carol wants.