I have always resented my siblings since I was born because I feel they ruined my relationship with my mom.
Has you or your mom ever talked to you about this?
I did but she never seems to think they did it on purpose.
Maybe she is right and they didn't do it on purpose. I don't think they would want to ruin your relationship.
She also said "If you give up on your siblings then I'm going to leave you."
That's a really tough situation to deal with. I believe it's worth it to try again, and really ask what your siblings are doing. You are all family, and should be creating happy memories and this could be the chance at it.