I had this happen the other day, but it was with a Sim's ex-lover (he was wooing two women at once, got both knocked up twice, then married the first one I went after). He'd claimed his two kids from her, so for my story I imagined that she had basically invited herself in with the expectation that if she stayed long enough she'd be invited to move in so she could be with her kids. They barely had enough space for the family to sleep, though, and I got sick of her taking a spot on the double bed so neither of my adult sims could sleep in it. I had the ex-lovers fight and fight and fight some more, then had the wife start arguing with her, then the kids... Nothing. Eventually the wife took her to the park and abandoned her there.
I no longer invite that particular sim into the house EVER.