Partially a rant at how awful the BA website is but mostly looking for advice on how I can resolve the following please:
Goal - Add my 5 month old daughter to my household account and book LGW>SKG return Avios flight.
- I needed to remove one person from my household account in order to add my daughter, as I knew I was at the 7 person limit
- Logged in fine but when viewing household account it only shows myself and my eldest daughter, no one else

- Managed to get hold of someone on the BA customer phone line who could see all the members and removed one for me.
- Logged back into my account and was able to send a new invitation for my youngest daughter, but once I clicked send all record of it vanished with the household account still only showing my eldest daughter and I.
- No email received for the invitation.
- I then gave up for the day...
Next Day
- invitation email was received 8 hours later at 1am...
- Invitation link prompts me to fill in the primary account holders DOB, no issue, and then asked to complete all the new joiner details.
- I click submit and then get this error...

- I then try calling BA again but when I get to the automated bit that asked me "what kind of account do you have, you can say blue, silver, or gold account" and I say "blue account" it just keeps repeating itself over and over again
- Eventually I just say "agent" at which point it says they are too busy and hangs up on me
I've tried multiple browsers and multiple device types to edit the household account but all have the same problem of either not being able to see all the members or unable to submit the new joiner form. There are only a few seats left for the Avios flight we need so I'm not sure how to proceed.
Is it best if I just temporarily add my youngest daughter to the friends and family list without an account so I can get the flight booked? I don't think she will have an opportunity to earn Avios between now the the SKG flight anyway
Any advice gratefully received!