In reply to Lynsety:
ten year old bike - sounds like one of mine
I did similar commute in sunny Ayrshire, initially changed forks on hardtail over to rigid, made a huge difference - get the gearing sorted, slick tyres and you will be fine
Once kids grow out of the trailer buy yourself a second hand roadbike, I got one for £80 and its great for the commute
Or man up and get yourself a single speed, that will stop all the gear problems (once grit/salt get in the gears every day over winter wrecks havoc on them) and will also get you fitter - perhaps wait until you not got the trailer though
If the cost of changing forks to rigid is high look at getting a second hand rigid fork bike - sometimes cheaper to buy replacement bike than it is to change specific parts on a bike unfortunately, especially if there is a bike recycle place nearby