Will the property tax assessment rate increase from its very low rate to the current and much higher riate when I buy out my sisters portion of our mothers home which we all inherited?

Probably not.

Is should not increase but simplify to changing the names on the deed. If you treat this as a purchase rather than an interfamily arrangement you may catch the eye of your assessor.

That is an issue, but the sale is not normally reported to the assessor.

I just picked up on a word I missed in the original post. "... which we all inherited" Now it seems there may be more than brother and sister involved. The result will probably be OK.

I agree!