Vent/advice husbands cousin moving in 😤😥

I have a two week old and my husband is at the end of his leave. His cousin just left her boyfriend and she is sitting in our living room right now and apparently we're the only place she has to go...except this is the second time she's ever visited us since moving nearby 6 months ago.
My husband wants to let her stay, but I'm so worried that this will turn into weeks or months and I'll spend my maternity leave dealing with this. It's bad enough my husband has to spend the last of his leave dealing with her drama!
A little background - she has had 4-5 boyfriends over the past two years. Always moves too fast and moves in with them the has a big dramatic breakup. She's young and whatever, but seriously this is not an okay time for her to be pulling this. I love that my husband wants to help his family, but I'm so annoyed. We've just got a breast feeding schedule worked out and I've finally need getting more sleep. Okay, rant over 😣😢