My sister and I are having trouble with the banks accepting the POA because it list us as ‘jointly’. Mom refuses to change it.

My sib and my experience was you had to get a guardianship. That is what banks want. A POA is very easy to get. Not so with gship. However, many businesses will only deal with POA,because they don't know that gship trumps a POA.

What reasons are the banks giving in regards to why they will not accept the POA because it list your sister and you as ‘jointly’?  Is it because BOTH of you will have to sign ALL checks and deposit slips?

Are you having any problems with any other companies because of the "Joint POA"?

Is your Mom's Joint Power of Attorney written so that your sister and you can act independently of each other or do you BOTH need to agree on all decisions and co-sign all legal documents on your Mom's behalf?

{The word "severally" needs to be written in the power of attorney form, appropriately placed, to enable your agents to work separately of each other. When this occurs your agents are acting "jointly and severally".}
http://www.estate-planning-hub.com/joint-power-of-attorney.html

If your Mom is receiving Social Security benefits, your sister or you will need to have your Mom appoint one of you to become your Mom's "Representative Payee" for Social Security as SS does not acknowledge any POA documents. 

Copy and paste these websites to your browser:

https://socialsecurityintelligence.com/social-security-power-of-attorney/

https://www.ssa.gov/pubs/EN-05-10076.pdf ;
(Social Security Administration publication called  "A Guide For Representative Payees".)

Then she can't change the POA. Her doctor has now stated she is incompetent so she in incapable if making informed choices. The next step would be a conservatorship to handle her finances.