How can I stop my cousin from talking my mother into signing a new POA?

First, a clarification:   is this your mother, or your mother-in-law?  You've used both terms.

Just curious:  how did you discover that your cousin is prying in your mother's financial asset status?   Is she asking your mother directly?  Or asking your husband?

Besides following Alva's excellent advice, I might (and probably would) find a way to have a private session with your cousin and explain sweetly that your mother's assets are private, and aren't the subject of family discussions.   If you're not comfortable with a face to face talk, a nice card with very delicate advice could be sent.  I do think in person conversation is better though; you can judge the other person's response.

Sometimes just a "why do you need to know" inquiry can stifle asset snooping attempts.

An alternate, more aggressive but not direct way to attempt to stop the inquisition is to ask your cousin if she's volunteering or available to help care for your mother, and if so, what can she offer in terms of assistance?

I do know though how prying some relatives can be and have had to devise very polite "none of your business" responses.    I often wonder if these kinds of relatives realize how inappropriate their behavior is.

I'd be talking straight to the cousin and telling him in no uncertain terms that Mom's competency is documented, her affairs are in order, and she has legal representation.

Then make sure all of that is true.

Without a diagnosis of some kind of decline, you need to understand that your mother is assumed to be of sound mind. Therefore she can assign anyone to be her POA. Certainly we cannot decide whether the cousin, who seems to see your Mom and have her trust is A) concerned for her, her financial safety and her future needs OR is B) up to some nefarious self serving machinations. You may have some other reason to distrust this person.
If you have not discussed with your mother POA, and her possible future needs for one, now is the time. Do you wish to do this work (it IS work); are you willing to pay bills for your Mom, keep meticulous records understanding that is your responsibility as a Fiduciary? Then now is the time to discuss this with your mother if she is of sound enough mind to do a POA and a will, etc. Are you even certain whether or not a DPOA is in a current will she may have?
The best way to avoid catastrophe is to act now while your Mother is able to understand your wish to protect her and your willingness to serve. Or at least to discuss changes you are seeing, and your wish to protect her.
If your mother and you do not have enough mutual trust to do this, then the sad fact is that she may in fact choose this cousin to be her advocate. Then, should you suspect abuse it would be your chore to pursue conservatorship in order to protect your Mother's finances and see to her diagnosis and care. Hopefully this can be avoided with some proactive honest discussion within the family.