Well trading only allows one ship to trade between two specific planets. There's a current bug that won't allow you to set up additional trade routes to your other planets from a partners planet without waiting a day or so.

I believe currently if you trade out of a fleet of trade vehicles it sets one of them on the trade route after which (when it's eventually fixed) you could select the fleet and set up another route to another of your planets for the next one and etc.

I haven't verified this yet however.