Your main ship cannot inherit either power or shields from entities docked to it. Power and shields only flow outwards from the main ship, not the other way around.
The essential idea of a 'missile drill' is that a first missile punches a hole, a second missile following right behind that one flys into that hole and detonates at the bottom of that one, making the hole deeper, then a third one flies into that hole and does the same, followed by a forth, then a fifth, etc.. This works best at close range before missiles have time to zig zag out of the straight line trajectory that they would otherwise have. At long range, even the best constructed missile drill simply becomes an ordinary missile volley that will pepper their target all over the place.
To build a missile drill, all you need to do is stagger the firing points of the respective missiles one in front of the other. It might be best to vary the stagger a bit a few blocks in all directions to make it harder for a single point defense turret to line up versus all of them, but they sill need to be close enough for them to fly into the holes made by the others. The missiles also need to be powerful enough to be certain to actually be able to punch holes through pierce hardened advanced armor, so they can't bee too small in terms of damage.
In my opinion, the best way to get a successful missile drill ship that can be AI piloted is to put the drill in a turret on a relatively small, relatively fast ship. The turret does not need to have a large axis of rotation as the ship itself can do the rotation. Give the ship itself 'only' a beam/cannon/ion weapon as a forward firing hull weapon. That weapon does not have to be large. The point is that the ship's AI will fly so as to engage with that hull mounted weapon. As the range of a beam/cannon is very short, it will basically fly to point blank range, where the missile drill will be most effective.
A missile drill should be built with missile/beam/explosive, but with no beam modules slaved. This will keep the missiles seeking, but also keep them firing every 15 seconds. You do not need the extra range for a missile drill. You might consider using missile/cannon instead, which will make them dumb fire. This will guarantee a straight trajectory but also mean that it might have a lot of difficulty hitting agile targets. Versus large ships though, such a ship/weapon could be a true nightmare once the shields go down.
If you want to get really funky, give the ship a pulse/cannon/ion weapon, A decent sized shield drain beam system, and a missile/cannon missile drill in a largely fixed turret. This will get the ship in really close, will work as effectively as possible bringing down the enemy's shields while reinforcing it's own, and once the shields go down, the missile cannon drill will be at such close range that it can't possibly miss.
