States can have some pretty strict laws about who and where a haircut can be given. I'm not sure it is legal in NY to do in-home cuts by an licensed stylist. I agree that you should just order a proper pair of scissors on amazon and do it for her -- if she has short hair and isn't picky about the outcome (and isn't even going out in public!) then hopefully she'll be ok with it. The right scissors will help a lot.
No, she is right. She should not go to a salon. I am now on my third homemade haircut and to tell the truth it isn't bad. Would you be comfortable watching some youtubes and watch how it is done. I bet you could do it! And I think we will be on lockdown so long that if it isn't perfect, Mom will not see it well, and it will grow out with a bit of time.
Does Mom have a regular stylist? If so, maybe she/he will come to her home. My GFs do it for regular clients.