I would not recommend a back-mounted child seat because I think it puts the weight up too high and makes the bike more unstable. Itâ€™s also bad for kidâ€™s necks when they fall asleep in those seats and their heads flop over. The seats for small children where they sit in front of the parent are good, but itâ€™s for small children (max 3 yrs), so they grow out of it quickly.
A double trailer is good because you can take both kids and take turns pulling the trailer. If possible get the kind that has a really sturdy connection with a ball on the trailer fitting into a socket attachment at the rear wheel, such as on a Chariot brand.
You can also consider a trail-a-bike for your older child. Your younger child can grow into it by the time the older one has their own bike. For short trips, if you already have a kids bike at your house, one of these trail-gators might work for you.