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. It’s also bad for kid’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 it’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.