Trying to read between the lines......
Were BA genuinely overbooked? If so, and they had to bump passengers, it would seem incredibly irresponsible for them to try and offload two minors.
On the other hand, as Hand Solo suggests, there seems to be some doubt as to whether they were involuntarily bumped. If they were made an offer, surely all they had to do was refuse and BA would have to ask for volunteers elsewhere.
All of which makes me wonder if the girls really were, as the story suggests, initially told they couldn't travel, full stop.
As to Ladbrokes, Mr Bell has a responsibility towards their shareholders. It strikes me as an abuse of his influence to use his employers travel budget as a weapon in what is essentially a personal disagreement with BA.