I was able to fit everything into the bike carriage and the very end of the rear carriage, resulting in a two person 'deluxe' carriage with a table.
I'm using an S-Brick instead of the IR receiver, so that may also make a difference in getting it to fit into the bicycle carriage.
Thanks CisFran and everyone else for the inspiration and pictures/instructions - these have helped me a lot.
I used the 9V battery idea from CisFran, and also took inspiration from this youtube video - https://www.youtube.com/watch?v=I1rVeBkKMJ0.