I have carried on a roll-aboard and a backpack (and sometimes a small bag of reading material) to ANA flights in coach and I have never been questioned or stopped. The rollaboard size-compliant (at least US) though probably would be over 7.5kg. I board in the premier lane, so that may help, but the family member will to if in F/J. I generally have not checked bags with ANA, but when I have they haven't assessed carryons for compliance as some European airlines do - and I don't see the "carry on luggage" tags some carriers issue. Bottom line, if bag #3 is generally compliant I would just carry it on. Family member could also gate check it at NRT to lighten the load for the rest of the flight . . . though definitely won't be stopped by UA (even with Japanese gate agents).

I haven't seen ANA ask people to gate check luggage - I guess Japanese flyers aren't as carry-on-heavy. Or maybe they do it only after I've boarded.