Wow, she takes advantage of you, and then when you call her out on it she tosses you out of the house?! What a princess! Sounds like she's just looking for a Mr. Mom to be her live in nanny so she can go live her life kid-free and hang with her girlfriends. They're not even your kids, and you're not married. You don't owe her shit, and she is being straight up unfair and unreasonable.
Do NOT give an inch on this, seriously. I'm not even sure why you'd want to be with someone like this but it's your life and your call. Do not live with her again until there are some serious ground rules laid down, as in you aren't watching her kids and picking up after her ass every night. If she can't wrap her head around it, I say move on and save yourself a headache.