With you being 61 and her being 80, it's time to practice acceptance from this point forward. Your mother will be jealous, petty, and insecure until the day she dies. She may be jealous that her husband enjoys spending time with you. She may be jealous that you're able to do things she can no longer do. She may be jealous because you're younger and in better health. It doesn't matter why she's envious; it just matters that you accept she is and not let it bother you. It has everything to do with her, not you.
I'm answering your question after a week-long visit with my 82-year-old mother. She's a deeply insecure woman who's always gotten easily jealous of others, especially my sister and me. She sees other people's happiness, achievements, wealth, and acquisitions as a personal affront. During her visit, she expressed envy that I have two teenage sons who are thriving academically and socially. Instead of complimenting me on my good parenting and their hard work, she constantly labeled us as being “so lucky.”
In the past, it would have bothered me but now I just let it go. In fact, it even makes me chuckle to myself. When I'm with her, I use the words of the spiritual writer, Eckhart Tolle, as a mantra: “Accept this moment as if you had chosen it.” Instead of fighting the situation, I learn from it and become a better person.
It's said that whoever causes us the most emotional pain is our greatest teacher. I imagine that you've learned many lessons from your mom's insecurity and jealousy. The fact that you put up with it in order to take your stepdad to his medical appointments says a lot about your honorable character.
I know that you wish your mom was different and you had a loving relationship with her. Yet, when you accept her with all her limitations, you'll let go of a lot of stress.