Can someone claim ownership for paying property taxes on property they do not own?

I am assuming that you are an interested party in the estate.  A beneficiary?  If you believe that an executor is acting improperly in the handling of the estate then you have the right in most states to petition the court for his removal and demand an accounting.  A deed gives you the legal right to property.  If the taxes were not paid the state would have placed a lien with penalties and interest on the property.  Sometimes there is a sale of the tax lien and there are instances when people try and assume ownership of property by obtaining ownership of the lien.  However, that is very difficult and may in fact be prohibited by your state law.  And it is also not what happened here.

You need to hire an attorney to take action and demand an accounting.  If there is no formal rental agreement I would argue that her paying the taxes was considered rent.  The executor has the obligation to protect estate assets.  There is an obvious conflict here.  The estate will have to defend against the daughter's claim. Also, if the executor is acting improperly he could be held personally liable.  A competent estate attorney in your area can help you figure this all out.