Another option is a Dutch-style trike or bike with a cabin for seating one or more children, along with your luggage. Often these have a way of attaching a baby car seat, so they can be used with even younger children than trailers. They are sturdily made and designed for carrying lots of weight, so they are geared appropriately.
York Bike Belles has a cycling families project, including sessions where you can try out different ways of transporting your child on a bike to find out what will work best for you:
York Bike Belles.
Happy Cycling!