Saying “love you” first to your family feels awkward exactly once. After that it’s just true out loud.

The awkwardness of saying it out loud is entirely front-loaded. It exists once, in the first instance, and then the sentence becomes ordinary and the family adjusts around it faster than you expect. Plenty of people wait for the other person to go first and end up never saying it at all.

Say it at the end of the next phone call, before you hang up. Do not explain why you are saying it. The second time will already feel like nothing.