I would like to answer a few of your questions and hopefully the answers will give you an idea of how to proceed.
Probate would be established where her primary residence was located. The real question is whether she established Butler County as primary residence or if it was just intended to be temporary.
Probate is required to access assets in your mother's name alone. If there are no such assets then you might not need to probate the will. It is important for you to make this initial determination because one the probate process is initiated you will be required to perform certain tasks and pay certain fees that you could possibly have avoided.
Even if there are assets in your mother's name alone you should decide if it is prudent to probate the estate. If the expenses are definitely greater than the assets you might determine that the process might be cost prohibitive. It would then be up to the creditors to go after the estate assets separately.