I think this sounds good on paper, and up to a point, I agree in principle. If the goal is to be mentally healthy, then chasing after anyone, even family, who shuns you or is not healthy for you is a poor decision.
I miss all my family. They don't talk to me. I miss my friends. I'd be less than human not to acknowledge the void and the scar.
My commitment to me is simply to be mature and as healthy as I can be. So yes, I do get melancholy. No, I try very hard to not allow their idiotic decisions to affect me in my day to day life. It's pretty much something I've let go of. I am not angry anymore. It just is.
I think it's a mistake to stay angry with anyone in my opinion. That just means they are influencing your life still, just in ways that you may not be aware of.
When you think about it, getting angry feeds into the GB narrative of "apostates". Tell them instead that you are going to work to get healthy in all aspects of your life, that you love them, you miss them, and that if they ever want to have a relationship, you'll be here for them. That has more impact IMO then telling them to f*ck off.