Jou_de: Situation: You built a ship. Maybe it was finished while you were somewhere else. But you want to fly the new ship.
But you cannot switch to the new ship, it even got added to another fleet. Even when you fly right in front of it, no go.

Step one: Merge fleet.
Go to "Company", (F5).
Check that "fleet" has the visible flag.
Click your trade fleet 1.
Click "edit".
Screen switched to "Fleet" menu (F6).
Click your "other" fleet, here "Trade Fleet 2".
Click "Merge".

Step two: Switch the ship.
Go to "Sector Info" (F2).
Click your other ship.
Option "Fly" is available now.

You can then split the fleet again, and send your older smaller ship to do some other regular job.

It took me a while, so I guess others may need that info too. Visual way attached.