On my first family flight out after the initial lockdown (no BAEC status) I got assigned seats all over the place at OLCI, issues with uploading the COVID document as Passport did not match BA ticket details (passports has the kids middle name, BA profile and every ticket I ever bought, do not) and was travelling with a 5 and 7 years old. After 50 minutes on the phone to speak to someone at BA, I was told that I could call a week or so before for them to sort out the seats and have the kids seating next to me. So they arranged this for the return but could not help for the flight departing the following day.