Why would you set up two people to be POA?

Well, it really all depends on your family dynamics. My brother and I were named "jointly and severally", which means either one of us alone or both together could get the job done. At the time Mom made up her POA documents it wasn't clear which one of us would be in the best position to serve, although it has been a bit of a hassle since my brother passed away.
As for your sister abusing her position, that is a totally separate issue. Although paying herself for your mother's care isn't necessarily wrong it can certainly cause problems if mom needs medicaid and there wasn't a proper contract drawn up and receipts weren't kept.

I would never appoint two people as my POA. I would (and did) appoint a primary and a backup POA.

When there are 2 POAs, they are supposed to BOTH make decisions together. They are supposed to agree on any expenditures, ect. How is it that the other POA made financial decisions independently?

Was your loved living with the other POA? Was this POA providing caregiving? This is not against Medicaid rules, but if there is no contract in place spelling out what is provided and what the cost is, then it would be considered gifting, and would invoke a penalty.

I suggest that you consult an Elder Law attorney (specialty is important!) and learn if there are ways to appeal the Medicaid ruling. It would probably involve proving the Loved One's money was used for her care. You can spend LO's money to see the lawyer.

When you say the other POA has taken and spent your mother's money for keeping her...

That is what you are actually meant to do. Unless you mean the other POA has been spending money on other things, not on your mother's keep?

I'm a little confused because your profile says that your mother is living at your home. So if you're planning to resign your POA, and your mother is not able to apply for Medicaid, and the other POA has misappropriated your mother's money (which is criminal, by the way)... how is this all going to work? What's your plan for your mother's care?

Read your POA and see if there are instructions for removing yourself as your mothers POA. Check the laws of your state. Perhaps a call to the attorney who prepared the POA could tell you. You may have a responsibility to take action against the other POA as you appear to have known for awhile that her affairs were not being handled properly. Objecting to mismanagement is one thing. Doing something about it is another.
I'm sorry for your trouble.