You gotten a lot of good advice so far. Gatorsmom and dogman advice is right on, even down to not taking this personally. Which I know is a lot easier said than done.
You’re a girl, she’s a girl and both of you share the same grandma who have treated quite differently. That’s not on you, but it’s also not on Jane. It’s on your grandmother who have passed on. This is why your brother isn’t getting the same treatment cuz in her eyes and mind, his experiences is very different from both of yours. It may be irrational or unfair to you, but that is how Jane is looking back and remembering all of this. Alcoholism is tough. Childhood trauma is real.
It’s ok if you don’t want to put any effort into your relationship with Jane anymore, as it does sound tough on you. The back and forth and rollercoaster nature of it. I wouldn’t focus on rest of family’s relationships with Jane, your mothers, brother and your kids to Jane’s kids. Maybe one day your kids and James kids may have a relationship when they’re older as it’ll be easier to do so without having either you or Jane to manage (expectations too!) that.
You can write a letter sharing how you really feel, what you want going forward and put it away. It may help you feel a sense of peace or closure when it comes to Jane.
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Mummy to DS1-6/11 and DS2-1/14