I'm moving Mother from an independent living facility to assisted living in another facility. How much notice?

What is required by any facility, esp. independent and assisted, is not regulated by the same laws that regulate nursing homes in a state. They are businesses free to make their own rules for the most part. There is usually a contract on entry to the above; check your Mom's contract. Get things in writing when you are able.

I would think that would depend on the contract that was signed.