Safe to travel cross country with 3 and a half month old?

Is it safe to travel cross country with 3 and a half month old? I live on the east coast and my brother in law is getting married on the west coast (husband's brother)

It will involve flying with a stop in the Midwest and then driving three hours in a rental car once we land

Is it safe to bring a 3 month old on flights like that? Without the second set of vaccines? Can they sit all day like that?

Has anyone done it? I'm dreading it. I'm dreading his sleep schedule getting all messed up, too, them having to return back home to work with it all messed up