Establishing family ties means having some form of contact, even if it is by phone. There is no limit for how often one must visit his relatives to not fall in sin. Rather, it varies from person to person. Continue contacting them over the phone, send them gifts etc, and you're not cutting family ties.
As for visiting them in person, it is what is conventionally known as upholding family ties. You have to figure out a way to overcome your awkwardness. I used to avoid family meetings back in the days. Now I go myself and visit them whenever the opportunity is given. How to overcome it is an issue you have to tackle yourself. Your decision is a very good start, and I pray that Allaah makes it easy for you.
As for visiting them in person, it is what is conventionally known as upholding family ties. You have to figure out a way to overcome your awkwardness. I used to avoid family meetings back in the days. Now I go myself and visit them whenever the opportunity is given. How to overcome it is an issue you have to tackle yourself. Your decision is a very good start, and I pray that Allaah makes it easy for you.