Marka 55 didn't mention (or me) the 423 bus. This is also in the free bus zone and goes to Hatton Cross but goes around the north side of the airport so will take longer but this bus stops almost next to the Hilton Garden hotel. Just a few yards walk. May be the best option given the op has luggage and a small child. Get the 285 opposite side of the road back to T3. Also the 555 but there are less frequent.
I'm confused about the luggage. I had assumed we would not have to collect our luggage. Also, the BA website says "If you have booked all your flights under one booking with the same ticket number, you only need to check in your bags once when you start your journey then collect them at your final destination." This is the case for us. However, I understand that since we are leaving out of T3 after having arrived to T5 we might have to collect our luggage. I sure hope not, as that would add inconvenience and time to recheck it. The BA offices are not open in my country on the weekend so I will check with them tomorrow on this topic.
