Just to reply on the avios query, as stated above there is no negotiation in terms of compensation, you were provided with a hotel for the night, you are entitled to €600 each (not sure on the infant element), and you were transported to your destination, albeit 24hrs later. However, BA are offering avios in place of cash, 50K per person, so if the avios is more important to you, that will probably be an option available to you once you lodge your EC/261 claim.
Pilot37