I think that one way to make progress with your issue is by helping your child who may have inherited or picked up on a pattern of yours or your spouse's.
The way I helped my child build a relationship with a relative he didn't see very often was, I would set him up on a phone call with the person and when conversation was slowing, I would suggest a topic. In our case things were complicated by the relative being my mother-in-law, which meant she was monolingual in a language I'm not strong in. But it was very helpful to get the child in the right language groove for the phone call. So I would propose calling Omi in German, and I'd give the topic prompts in German. I must say my mother-in-law was very cooperative -- tolerant of our pidgin German, and also responding very positively to nonsense talk and bragging.
Also, sometimes I flipped it and had a pre-conversation with Omi while the child was out of hearing, in which I suggested asking the child about A, B and C.
Here's another example. My spouse never had play dates growing up and has a hard time striking up new friendships. So, I made a point of setting up playdates for my children.
Speaking of playing, you can help your child get to know a relative by the three of you playing together. With a little practice you can get comfortable incorporating the relative into your play activity by using your parent voice with the relative, while you are in play mode.
What to play? I'll mention some ideas here to tie in with another question I think you asked. Classic play activities include, depending on the age: water play, "washing" a set of play dishes, buying and selling at a pretend store, Playmobile characters and props (e.g. a hospital set, a veterinarian set -- ask lots of questions and let the child direct the story), hide and go seek (the favorite hiding place from my younger son's point of view, was under the covers in his bed. If he hid there, I would drag it out to his heart's content by sitting on him, tired out from having looked for him everywhere. Tip: verbalize liberally while looking, e.g. "Where can (name) be? I've looked for him in (list that keeps growing). I'm getting tired! I'm going to sit and rest and try to think of more placed to look!")