If you're looking for a lot of hauling capacity and carrying children, I'd personally look into a trailer rather than a trike. The trailer will give you a lot of capacity, but you can ride without it if you're not hauling anything.
As to the bicycle, it depends on your riding conditions. I'm not familiar with Leeds so I don't know if you have to contend with wind, hills or snow. If you have wind or hills, you'll want something with a good range of gearing for climbing. I'd be most interested in a touring bike since it has the gearing and the durability. If you have a lot of snow or on rough roads, look for something with wider tires and good tread. An older mountain bike without suspension or a hybrid would be ideal if you need the wider tires.