Keep her while you're finding a replacement (so you have coverage), or - given what you're describing - get a temporary nanny through an agency until you find a permanent solution.
She sounds awful - I would react the same way you are.
I agree about modifying your contract. I don't think two weeks severance when someone is still in a trial period is necessary and there should always be the ability to terminate for cause (without provision of severance).
Glad you realized it quickly at least! It would only get worse over time.
When I was interviewing nannies we met one who was fantastic in tons of ways, and very experienced. But when we had her in our house and she started criticizing how we had the changing station set up that was the end. "Well, I'll have to fix this right away". Oh really? Nice to meet you...
Hope you find someone great.