My nature is exactly the same. If a friend breaks my trust once, I will not talk to him for the rest of my life nor will I be able to trust him. I was friends with a cousin for 13 years, but he said some wrong things about our friendship, which I came to know from one place and then I confirmed them. When they were true, I ended contact with that cousin because when there is feeling, there is attachment and when such things happen, then love ends completely.
It's difficult when a family member breaks trust but I think it needs to be treated the same.