Can I move my aunt to a different SNF if she is not getting quality care at the one she's at now?

Oh wow. The fellow I cared for had this situation,
he wanted to be moved. The attending physician flat out refused to sign the orders. Further...no physician at the other facilities would admit under the protest of the existing physician.

I had to get him discharged completely.....against medical advice. Then, had trouble finding another facility that would take him because he didn’t have a physicians order.

what a huge mess.

I was his sole caregiver for about 6 months. Until he had to go the emergency room once again....then I refused to take him back.

I just responded to a similar question recently.  Se my first, enumerated answer of 2-15.  

https://www.agingcare.com/questions/what-are-the-next-steps-or-options-for-my-mil-who-lives-4-hours-away-and-rapidly-declining-health-456398.htm?orderby=recent&page=1#1169084

It's a different situation, but with issues on moving from one facility to another.   Skip the paragraphs that don't apply and start with the second paragraph in Item No. 1.     I'm too lazy to retype the suggestions here!

If she’s competent to make decisions for herself and wants to move then she certainly can move. If she can’t make decisions for herself and you have POA then you have the right to move her.