I am sorry to hear of your situation, and I wish the young girl luck and hope the treatment in the USA goes well.

With regards to upgrades, it does happen sometimes but BA will not pre upgrade someone. It's possible on the day though. Does she or anyone travelling have any medical requests or meal requests on the booking, or any wheelchair assistance? as these do limit the chance of any upgrade. Also does anyone in the party have status?

I wish you and your family the best, and good luck with an upgrade.
joejet