I think the reason you feel better is because you are giving yourself closure. Accepting what you can't change is a huge part of healing. It sounds like a enormous amount of pain you carry with regard to their indifference towards you. By cutting ties, you are letting them go and accepting the inability to change their indifference.
I cut ties with my immediate family and extended family, including 26 cousins, all of whom lived less than 3 hours from me. In spite of having mom and 3 brothers, 10 aunts and 10 uncles and 26 cousins and 5 second cousins, I opted not to invite even one of them to my wedding. I wasn't angry at any of them.
This worked for me. I'm not a big fan of pretending to care about each other. Their indifference towards me always made me uncomfortable. I'd rather be alone than be with people I know are indifferent towards me. One shouldn't feel lonely in the presence of loved ones. But it happens more than you think it does.
I believe if something or someone hurts you more than they uplift you, it's better to remove them from your life.
My mother died in 2013, she had 6 remaining siblings alive at the time. None of them went to see her when she was dying. It took 2 months for her to die. One of her siblings was in the same hospital having tests done when she was dying. Knowing she was 2 floors above him dying when he was getting his tests done changed nothing, he still didn't go to see her.
I chose to remove her and my entire extended family from my life in 1999. Her last act towards me during her last few years of life was to ensure her hatred towards me lived on past her death. Three of my uncles have inherited my mother's hatred towards me. One of them said "I feel like going down there and breaking her legs." So her hatred towards me lives on, even though she died three years ago. I don't live with just indifference, I live with hatred. I haven't even seen my uncle for over twenty years, yet he hates me now.
My mother was a prolific liar and at the end of her life no one wanted to be around her. She was diagnosed with Narcissistic Personality Disorder in 2001. So manipulation, control, lying, alienation and an inability to love were all parts of who she was. I felt a tremendous relief when the psychiatric nurse told me she was incapable of love. I realised it's not that she withheld her love from me, she was incapable of love. There's a huge freedom in knowing the truth.
Sorry I've made this so much about me, but my situation is similar to yours. If being with family doesn't do anything for you, but the indifference hurts you, perhaps this is the best decision for you.