I doubt its posssible, ships and stations are different data types within the game.
However it could be possible to modify one of the mission scripts to accomodate this. As you know the missions are capable of placing you indifferent locations in spce with different objects around. You could probably set it up so your battleship was a base and talking to a particular character at the bar would offer you the chance to fly your fighter. This would spawn you to space as a fighter at the battleships current location. When you docked with the battleship you could talk to another bar character which offer you the chance to spawn to space as a battleship and remove the battleship base you were landed at. How you would switch from flying your battleship to being docked at it tho would be a problem. One possibility would be to have some specific piece of cargo on the battleship - destruction of a piece of cargo can act as a script trigger so you could eject and then destroy it to 'park' your battleship.
There are many problems with this method tho. Firstly i know you can set it to spawn things to locations but only ever preset location so idont know how you would get it to spawn your battleship base at the position you are in in space when you 'park' it. Loadouts are another problem, the only time i can think of when it messes around with your ship is right at the start when you first get your ship. It sets the ship as the nickname in shiparch.ini and takes the loadout from loadouts.ini. So while you could set it to spawn you to space as a fighter via a character popup i dont know how you would get it to remember your loadout, it would have to just pick a preset one. Same would go for spawning as a battleship. The other main problem is the fact you would have to hihack a mission script for it. As far as i can see it would have to be a storyline mission 'cause the random missions dont look like they have much scope for change. You could always add it as a mission post storyline.
Anyway thats enough of a rant, in the spoiler forum too of all places
Short answer : No i dont know of any mod that would let you do this.