If the cat takes to it, maybe you and your Mom can "share" the cat. She could stay with you part of the time, and your Mom the part of the time. That way, you could keep track of the cat. Truthfully, the only things that seem less than good care are kitty as an "outdoor" cat and perhaps not enough attention.
Hopefully, outdoor doesn't really mean she lives outside 24/7. Being outdoors at night is NOT good for cats. But, the ability to go in and out is basically the ideal life for a cat and we have had cats live for 20 years with very happy lives this way. Our oldest cat is now 17 and would be terribly unhappy if kept indoors at all times.
I also do not do vaccinations anymore. We had a cat develop a very aggressive tumor on the back of her rear leg, and the vet suggested it might have been a "vaccine-induced" tumor. Cats are apparently very sensitive to anything that pierces or goes under the skin and this is why vets were putting one sort of vaccine in the shoulder and the other type into the rear leg muscle - to track the incidences of tumors. I may get the distemper vaccine done because we are rescuing kittens lately and that vaccine protects against some of the "cold viruses" in cats . . . maybe.
If you can't take the kitty part of the time, check up on her. I am wondering what you actually spent $400 on? Sometimes vets just do things, even if they are not warranted. We also don't take cats to the vet unless they are showing signs of not feeling quite right, but you need to keep track of what "sick" is: if they are too quiet; or lethargic; or won't eat - they are sick.
Ask Mom to bring kitty inside at night, and also watch her closely for anything that does't seem right. But, maybe she is right in her assessment that the cat is 15 and is alright. Unless she has something wrong with her or develops tell-tale symptoms, she may be fine. After about 16, however, she ought to go in once in awhile and especially if her kidney values go out of whack.
You aren't a bad person for moving out, but you might be worrying a bit too much. Sometimes it's hard not to worry, and especially if you are the mothering type. Just visit kitty once in awhile and pet her while you are there.