I’ve only experienced a situation like this where BA generously extended rebooking privileges you wouldn’t ordinarily have had when cash was involved. They said to us if your new booking is more expensive you pay the difference, if it’s cheaper you get the refund, On this basis I’d say it’s reasonable for BA to want award inventory for the rebooking as they are extending the life of a ticket that otherwise would lose 100% value if you didn’t travel. So in this case retrospectively it seems the best option would have been to cancel the trip and get a refund less the fee of GBP 35 equivalent pp.

I don’t think you are due any restitution from BA for any extra costs. They’ve done nothing wrong here indeed have gone over and above by offering a free rebooking given the unfortunate circumstances, You could also say that you’d have incurred these additional costs if you cancelled the booking with BA.

I'm glad your little one is recovering it would seem the learning point from here is to make sure you have adequate insurance on such trips going forward which I know is difficult as a lot of policies don’t cover mileage bookings as they have no cash value.