Doctors won't diagnose my mother incompetent. She is spending all her money and not paying her bills. Any advice?

Mstrbill is correct. These filial laws are antiquated. Rarely used and if they are, childrens ability to support a parent is taken under consideration.

I too don't understand why the AL can't evict her. This is a private facility. Maybe they can help u get a diagnosis. They can evaluate Mom and if they have doctor associated with the facility, he/she can declare her incompetent. Or, the facility can call in APS explaining the children cannot help because they have health problems of their own. At this point, you can allow the State to take over Moms care. A State guardian will be assigned to her and that person will see that she is cared for. You can also call APS.

Make sure with your siblings that you do a formal declaration in the probate court (or sometimes the family court) in her area stating that she must become a ward of the state because none of you will take on the legal responsibility. If you have her POA the court will remove you from it if it is your wish.
Your mother is in AL so she is not in the street. Surely they automatically withdraw from her bank account to pay her bills there.
In the meantime, do not give her a cent. If the AL starts seeing that she can't meet the bills anymore, they will take action. Let them.

I wouldn't worry about that Texas law, those laws are not enforced unless children are very wealthy, in fact I've never heard of these laws being enacted except once in a very unusual case. In your case, if you have little money to give, you are not going to be forced to pay, nor are your siblings. So please don't worry about it.

"Doctors won't diagnose my mother incompetent."

Did you talk to her doctor or read her chart yourself? Where are you getting this info? If it's from your Mom's lips I would question it.

How is she competent yet is blowing through money? Does she have an addiction problem?

No creditor can come after you if your name doesn't appear jointly on a contract, like on a loan or credit card. Don't answer calls from creditors or listen to their lies -- they'll say anything to scare someone in paying.

Your Mom is on her own. You stated "The assisted living place will not evict her, her Medicaid/Medicare will not pay for state funded facility..." this is confusing. No facility will keep her without a payer. When she runs out of money then maybe the facility will apply for Medicaid for her? Why is she in AL if she's competent?

Do not pay anything for her or this will ruin you. It is unsustainable so don't even try.

Texas is NOT a filial state; a filial state is one which requires a child to provide for the housing, medical needs, food and clothing for indigent parents. I think your mother is on her own to be responsible for her financial wrongdoings entirely.

Best of luck to you.