So if it's an International long-haul flight, then there's no complimentary upgrade for EP at all (unless you are going to Mexico or the Caribbean). You don't want to use SWUs on reservations for people with no status, that means they are the last in line to be cleared, someone else with a Gold status requesting an "upgrade with miles" will be ahead of your SWUs applied to none-status members.

In my experience (I'm EP), what I do when I travel to Europe or S. Am with my wife and kid is I book 1 reservation with 3 main cabin tickets, then call and apply 3 SWUs to the reservation (or you can also apply "upgrade with miles" or a combo of 2 SWU and 1 upgrade with mile, it works the same as SWU if the upgrade is waitlisted). Since I'm on the reservation, my EP status applies to all 3 tickets waitlisted to be upgraded, so all 3 people are first in line if any business class seats are unsold or no-show on the day of the flight. Sometimes there's only 1 or 2 seats open for waitlist, then AA will ask you if you want to split up and take the 1 or 2 seats. In that case one of the adult can go upfront, or go upfront with the kid. I've also had a scenario where there was no business upgrade available, but there was 2 premium economy seats, and they gave me the 2 premium economy, but didn't take the SWUs out of my account (since it wasn't a business upgrade). I don't think you are guaranteed to be given any open premium economy seats, it was a gate agent decision so it's worth saying hi nicely and ask what's going on with your waitlist when you get to the gate.