I have this issue with being unable to dock at Trading Stations too.
At first I assumed the bays were full but I've since realised that all Trading Stations I've tried are undockable. If I try manually I get told I am unable to dock at this time. Using autopilot it will fly circles around the station forever. I've no other ship docked at the trading stations. I see no evidence of any ships docked at them. If there are they never leave.
I had this issue when the game was unmodded. I've since added the Bonus Pack for AP but this made no difference. I am not using any other mods.
I've uploaded my save game
here.. This is particularly annoying as it is making it very difficult to complete various missions in the plot to retrieve items and if what I read in this thread are true I'll eventually hit a point of being unable to continue the plot due to this issue.
From what I've read above starting a new save may fix it but I've already put ten hours of play into this game and it really isn't a solution for me.