I'd recommend putting one of the tickets on hold first, then the other if possible, making sure they both match up, confirm everything, and then book both. AA allows holding their award tickets for 5 days, delta does 48 hour holds (but they can be unreliable if you want to make changes), Continental only allows a 72 hour hold if you don't have enough miles in your account (easy since yours are in UA), United allows a 72 hour hold (easier since your miles are in UA).

I'd say book AA/CX/JL tickets with AA miles for yourself and your son and book you fiance and her daughter together using UA miles (you'd have to get a few more as it's 32,500/person in Y).