I have found BA to be very good when you you ask to complete the party (TCP?) and will look at seats that are blocked for other reasons. If you give them enough time they can proactively work it out. Where I as a parent have less sympathy is people who had options to purchase or organise and just leave it to the airport to sort out their disorganisation. I acknowledge that sometimes families are rebooked (irrop, canx etc) and then you just try to do your best.