This caught my eye...
"The last 90 minutes have been the most stressful I’ve ever experienced whilst travelling and I’m visibly upset, crying in the middle of the check-in hall. I’d put so much effort in to making this holiday perfect, a once in a lifetime trip that we’d all remember forever and it was being so spectacularly ruined right at the last minute."
This is bloody a first world problem. It's your return from your holidays. How can a return flight problem spoil your entire trip? Just take it as an amusing story you can tell your grandchildren.
Let me tell you what happened here... there was a communication problem with IB and BA system. This is not new, it happens more often than not - both IB and BA now this, but they don't bother about it because it costs money.