Am I overprotective?

How about, "yes, you can visit" and "no it can't be alone. My presence will reassure Mom."

I wouldn't worry about the visit doing any harm to Mom.

Michou, or your Mom might recognize your cousin. Whatever you all do, don't make this into a quiz for your Mom.

Tell your cousin what might happen, do not quiz Mom unless Mom does recognized her. Otherwise, your cousin could be a "new friend" coming to visit. If Mom seems uncomfortable, then that is a clue that your cousin should try another time, maybe at a different time of day.

I remember my Dad being pretty sharp in the mornings and early afternoons, but by 4pm his "sundowning" would take over.

Do you like this cousin? Is she someone you know reasonably well and would basically trust that she is being just a kind person who wants to stop by to brighten the day of an elderly relative? Or is there a doubt in your mind about her? (Like, why does she want to visit her alone?) If there is a doubt, trust your instincts.

Seems like you have been given good advice already.
I agree with all the above.
Visit might be beneficial for your Mom as long as you are there with her, monitoring the visit. And the cousin understands that she may or may not be known.
Best wishes and May God bless.

People rant all the time that nobody ever visits. I can understand your impulse to preserve your mom's privacy, (I know that my mom would be horrified at the shape she is in now) but it is what it is. If she has never dealt with dementia then I imagine that your cousin will be more traumatized than your mom if the visit goes badly, and if it goes well then your mom will have been entertained for a half hour.

Michou, can you put a name to your fears? Are you afraid this person is going to say something hurtful? Try to get mom's money?

I don’t think you're being overprotective. You know what your Mom can and cannot tolerate emotionally and there are many posts here regarding relatives going behind caregivers backs for nefarious reasons. There are no sneaky/questionable relatives in our family but still there are very few people I would encourage/allow to visit my Mom without me present to help direct the visit so it’s entertaining and not overwhelming. My DH and her previous personal caregiver are on the short list. Other relatives and friends are not. "Thanks for wanting to see her. Let me know when you’d like to come and I"ll meet you there". If someone insisted on seeing her alone? Not happening. My concern is how would you know if she visited without you? Can you speak to the staff about that?

Precision : I would be less reluctant if it was any of my in law that have asked, because they love her and still gave gifts and cards and she loves them and asks theirs news regularly.

Dear Michou,

It is good of you to look out for your mom. From my own experience, I feel the elderly need more visitors not fewer. It's good of your cousin to think of your mom and hopefully with some advance warnings, it will be a good visit.

From the other side of the fence, it might be a training visit for the cousin. The cousin might be really looking for some insight into one of her own direct family members or for her/his self to see what cuz is in for.