I think you are being more than fair and can leave this relationship with a clear conscience. No severance necessary. Give her the 4 vacation days, and if you like, let her keep the $400 as a thank you gift. Tell her you'll give her an excellent reference.
I let a nanny go and gave, if I remember correctly, 5 weeks notice. Our contract said that either of us had to give 2 weeks notice. I didn't give her a severance, but I gave her a little more in her final paycheck and found her her new position. I wanted to help her find a new position, so I posted ads for her and posted her info on my mom meetup group message boards. It turns out her next employer came from one of my mom groups.
You're doing more than I did, so I think you are fine.