Good on you getting your mom into a better living situation. Unless her new pals are spendypants, you may find she doesn't come to you as often for money as she may not spend as much on fluff to help fill her days. Hopefully they are all careful with their money, so peer pressure will help her keep miscellaneous spending to a minimum.
Property taxes here in NH are very high as we don't have any income tax. It varies by town and hers is about to go up by a few more hundred dollars, mostly due to the school system. When she first discussed selling her house, it partly was to move closer to her friends and partly to get somewhere with a lower tax rate. Unfortunately, because of all the extras she wants on the new place, for example, to give a large workshop to my brother, she likely won't find she saves much more than $10-15 a month on the taxes (none of which he contributes to).
My Amazon Prime account has saved us a lot over the years. If we can't find something locally at a reasonable price, we would otherwise have to travel an hour one way to get to another large enough city where maybe we could find it at a price we liked. It started with small things like vanilla beans so she could make a new batch of vanilla extract. It grew as I always offered to check on pricing for something she was complaining about availability or cost and often found I could get things cheaper for her. She likes the idea of getting deals so that helps.
But she won't shop online herself, not even to just do a comparison of prices with local stores. Luckily, when I go over each week, we can sit together at her computer to check things out and order any necessities. As long as I do the work, she's content.
As your mom doesn't use the internet on her phone, could you help her find a more cost effective plan before her next renewal? Last I checked, AirVoice had cheaper plans for just voice and data. If you could shave off $20 a month there, I bet she's be tickled. Especially if you can equate the savings to a bill like the yearly vet checkup. Doubly so if you handled the changeover for her as then she wouldn't stress over doing it wrong. If she's nearby enough for you to spend part of a day doing so, that is. It'd also give her bragging rights with the neighbors about how thoughtful and helpful you are in saving her so much money with something she might otherwise find overwhelmingly complicated.
I remind myself all the time that it's baby steps for both of us. If she doesn't bite on a money saving idea, maybe I planted a seed for the next time. Maybe I figure out a better idea for next time. As you said in your initial post, they sacrificed for us and patiently trained us. Now it's our turn.