BA generally does not allow changes on speculative delays even they have a good idea that the flight has to do a longer route.
Your family will arrive sometime and as they need wheelchair assistance (I guess you booked this already) they will be last from the plane then escorted to flight connections, where either if the not delayed much will get to the original flight or they get rebooked to the new flight. BA and AA might have other services to reach final destination so it's not necessary they have to wait 24 hours. IF you could let us know the US destination people can help you what other options they might have as there could be some indirect option too, however it is more or less your choice which one you prefer. Bear in mind that if you have offered same day connection but you choose to stay overnight because that is a more convenient service BA will not paying for the hotel.
If overnight stay required flight connection might able to book a hotel for your family might not. However BA will pay the bill if you ending up booking one by yourself. BA will also has to pay for meals, transportation cost to and from the hotel. There is a dedicated thread we have for this. Keep in mind there is limits what BA pay and how much so Sofitel might be an option might not be depending on the cost. Sometimes Sofitel is significantly more expensive than other hotels so of course BA does not need to pay the more expensive one. Don't forget taxi fare will be paid by BA to and from the hotel so its not that bad.