The best way to renew a relationship with family after being disfellowshipped is to go make a success of yourself. I've seen this happen.
A witness kid was baptized when he was 14 or so. When he graduated High School he announced he no longer wanted to be a JW. This sent an earthquake through his family and congregation as his dad was an uber-elder, his mom had been a full time pioneer forever, and his sister had married a bethelite and moved to NYC. The son was disfellowshipped and shunned by everyone.
The disfellowshipped young man continued to live in the area. He married (no family attended or acknowledge the wedding), had a couple of kids (not acknowledge by family), and lived his life. He started a business and it turned out that the disfellowshipped man was quite the entrepreneur. Then his father, the elder, went to work for him. In fact, a few others in the congregation went to work in his company. They justified it by claiming they actually worked for the elder father, not the disfellowshipped son. Turns out they are one big happy family!
You may have heard that "living well is the best revenge." So that is my advice to anybody, live well and sooner or later the ones who are shunning you will turn up like nothing had ever happened.