I think there are two different things at play here:
- He has a busy, active social life and clearly values family time. This is a good, healthy thing.
- The issue the OP seems to have is that the relationships are not progressing beyond casual, sparse dates
I would say that the key to knowing if a relationship is going to work is progression. Its not really normal after one or two dates to put your entire social life on hold for that person, in fact, its a big red flag in my eyes and not healthy at all.
At the very beginning of a relationship, I would not expect the other person to be adjusting their life too much to accommodate me, and I wouldnt do it for them either. Thats way too much pressure to put on a brand new relationship with a person you dont really even know yet- if you start cancelling time with friends after the first couple of dates and then it doesnt work out then you're going to regret it. Personally, I cant stand people who drop their friends the moment they meet someone new.
That said, there should be an organic progression in a relationship whereby as time goes on, more importance/priority is shown to spending time together.
If say, after 3-4 months you are still being treated as an optional extra then its time to have a conversation about it or move on because that would show to me that the person only wanted something casual and wasnt interested in a long term relationship. I would expect that after 3-4 months of continuous dating we would be doing more things together, and plans would be made to integrate both of us into each others lives. If thats not happening, it doesnt make either of you wrong but it does show a mismatch in where you both see it heading. I wouldnt recommend talking about where things are heading at the beginning because thats a bit intense but you can interpret people's motivations through their actions and if its not progressing then I would take that as a huge sign that it wasnt going to.
A big part of this is knowing what you really want from a relationship, communicating this and moving on if the other person doesnt want the same.