No, the court cannot. Your MOM could have granted you various types of powers of attorney, a limited one, or a general one. People always forget how many types of powers of attorneys there are.
Now the courts can grant you only two types of Guardianships. One is Guardianship of the person. That’s to take care of HER. The other is the Guardianship of the estate. That’s to take care of her bills, her account, her payments, and possessions. That’s all you need really.
The nursing home isn’t asking for guardianship, are they? They just want the payments, and if you get the guardianship of the estate you’ll be the one writing checks.
Also you have to report an accounting once a year to make sure you have dealt with the money in her best interest, just file one with a cover sheet.
“How can I keep the state from taking it (money and property) if she goes into nursing home?”
Why would the state be taking money and property? Do they have a medicaid lien? For that, you need to see a lawyer.