If they have decided (or realised) that their family unit is happier being separate from the main family yet they are continually messaged to arrange visits or to be invited to gatherings they don't want to attend, that might explain why they 'snap'.
People have different expectations of how families should operate, and there appears to be a mismatch between yours and your brother's. If his view is that he doesn't want a lot of contact, and yours is that you want to persuade him to meet up, there is conflict. He's tried not responding to messages, tried just not turning up, but you keep trying to persuade him to act in accordance with your view of how families should work. Of course he 'snaps'.
You seem unable to accept that just having a different outlook is acceptable, and diagnose people who think differently from you of being controlling, jealous, anxious, depressed and unhappy. You mention the fact that they seem happy enough in their own little family as though that is peculiar - if they pick up on the judgements being made about them (or the fiancé in particular) then that could explain why they want to stay away.
That may all seem harsh, but your posts are very one-sided and judgemental, and I can't help thinking that this could explain your brother's reluctance to have a close relationship.