Actually, it isn't hard to figure.
If you go thru life expecting everyone to do what YOU would do, you're going to be solely disappointed.
While it makes perfect sense that anyone coming to see your mother at this point would "be on board"...the reality is that the only way your'e going to stop someone from entering that room without a mask is if you stand guard at the door. While I think it's quite rude for anyone to ignore such a simple request, I also consider that those who would enter without one have "their reasons"...and those "reasons" are things that I personally would likely agree with.
I'd put a mask on in that situation, but that's just me. Respect for your friends should never be off the table. Bear in mind that not everyone shunning the shot is "anti-vax"...most of us just want to sit back and see how this all plays out before (possibly) taking the plunge, pun intended. I don't fear the virus and more than likely that 80 year old friend of your mother doesn't either...that's the difference and there's no amount of shame, coercion, humiliation or even threat of exile that can change that. A "persuasive argument" presented without those things can work much better...and the persuasion is quite lacking.
Anyway...I wish you the best and sincerely hope your mom pulls thru.