This is a problem with many alternate designations on many durable powers of attorney — the power of attorney document doesn’t state clearly when the alternate should step in for the first designated agent. If it’s not clear from the document, third parties, such as banks and investment companies, are more likely to reject the power of attorney because they don’t want to accept liability. You should try to get a letter from your father’s doctor stating that he is incapacitated and not able to act any longer in his role.
Then, if you present that letter along with the durable power of attorney document, the financial institution may accept the power of attorney. If not, you’re probably better off going to court to seek conservatorship of your mother. It seems a bit disconnected to seek a court determination that your father is incapacitated to get authority to act for your mother who is incapacitated.