If price is not an issue, the Sofitel is very convenient especially with 3 children-you did not mention their ages and if they are good travelers or not- but regardless, you can use the free Heathrow express train from T3 to T5, Much easier to just hop on the train than lifting lots of carryon bags up onto a shuttle bus. And this should be much quicker than waiting for a shuttle bus.
follow the signs to the correct lift that will allow you to get to the enclosed pedestrian enclosed overpass to the hotel. This is really ideal especially if you have lots of carryon bags and a stroller for a young child.

The Sofitel will allow you to bring a luggage cart all the way from T5 to hotel check in, and they usually have luggage carts readily available for when you return back to T5.
I have done this twice and it was very convenient and with 3 children it would be a breeze for you