Unfortunately, they are correct that if they are the trustee and power of attorney and you are not either of those then you do not have authority to access accounts unless they have your name on them.
With that said, if you have found issues in the accounts like you described them using the money for themselves, etc. then you can move forward to protect your mother by reporting your concerns of financial abuse of your mother to adult protective services in your area or filing a petition with the court to request your mother be adjudicated incompetent and request a guardian and/or conservator be appointed to protect her financial interest.
Here is a link to the adult protective services agency in Utah. http://www.hsdaas.utah.gov/ap_referral.htm
Here is a link to information about appointment of a Guardian/Conservator in Utah. https://www.utcourts.gov/howto/seniors/BasicGuidelines-2007.pdf
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