Pre-covid I used to be able to check in for regular US flights when this happened without providing API, which I always gave at the airport. It’s a while ago now though and I don’t know if it’s changed.

But really I wouldn’t worry about seating. I understand why you do, ryanair (etc.) have conditioned everyone to be terrified, but BA systems do try to seat people together, and they get it right far more often than not. Particularly with under-12s, where you’re almost top of the list (and will find in practice that everyone else is moved around you). I flew this week on a shorthaul flight where 5 rows on a full flight were blocked - turned out it was to allow a group of 30 to sit together.