
Quoting
adjusterjack
She is your tenant, you are her landlord. Your written agreement specifies 60 days written notice so you are stuck with giving her 60 days written notice regardless of your trepidations.
If she stays past the 60 day deadline you will have to evict her through the courts.
If you want her out sooner try "cash for keys." That means offering her money as an inducement to move out sooner which may involve refunding the two months that she paid you and maybe more, depending on how desperate you are to get her out. If you go the "cash for keys" route, make sure you get a written agreement and don't hand over the money until she is out the door with ALL her stuff and the keys are in your hands (but change the locks anyway).
Anyway, congratulations, you're the first person besides me who I've seen use "recalcitrant" in a sentence. It's one of my favorite words.