I am looking for an explanation that allows for a reasonable purpose for both missiles and drones, but I will accept answers that try to dissuade me from either.
Adding additional armaments is permitted within this technology base within reason. Ships should not be overly armed to stay more in line with current-era warships than with hedgehogs.
Comnbat drones should be armed with similar weapons as point defence for ships.
A drone is anything remote-controlled or any autonomous object that can maneuver freely, but has lower maximum acceleration than missiles, and its primary purpose is not to impact or detonate itself.
A missile is anything that has a drive and tries to impact or detonate close to a target and does not fall under the general drone definition.
Technological Base for Scenario
Ships have access to hyperspace technology, but will require substantial cooldown before making a second jump or will need to eject the hyperspace core without taking on its excess energy ("emergency jump"). Per-jump distance is limited by position and vector calculations of the target. A certain amount of uncertainty regarding the location and vector is to be expected.
A target point in space for the jump is calculated relative to an object, with higher accuracy the closer it is to the drive. This way, the vessel will have a close enough velocity vector to the target so that it gains the necessary orbital velocity to stay there.
Combat vessels are armed with relativistic/near relativistic weaponry, especially mass drivers. They are also armed with nuclear weapons like bomb-pumped directional plasma devices and fusion bombs (in missiles).
The main defence mechanism is the barrier plane, an energy field of fixed size, either of rectangular or circular shape and little depth. Its size and strength directly correlate to the number of projectors and the distance to those projectors. The further away, the larger the area gets, but the weaker the barrier is. The more projectors in use for a single plane, the stronger it gets.
Sandwiching of planes is limited.
The loss of projectors resulting in less than three projectors per plane results in dissipation of said plane.
Obstructing the projector beams path has the same consequences as losing a projector for practical purposes with regards to the barrier plane.
Adding a projector to a plane without calibration results in plane destabilization. A non-trivial amount of time is needed to calibrate a projector group.
Each projector group can only sustain one plane at a time.
Enabling and disabling planes does take a non-trivial amount of time.
Planes are inertially locked to the ship and will move with it. They also have no mass.
Planes can reasonably withstand a hit from a relativistic mass driver or fusion device before collapsing.
Barrier planes are completely opaque to all kinds of radiation from either side of the plane.
Ships rely on observation drones to see the enemy while hiding behind their barriers or need to temporarily shift planes to be able to see through.
Ships may be equipped with lasers and high rof low velocity mass drivers as defence against drones and missiles (point defence).
Principally, the hyperspace technology could be used to transport things without a dedicated drive on the object, this could be achieved by a catapult, with the same restrictions as the drive technology. One could teleport missiles or drones to a sufficiently close location to the target that they can maneuver reasonably with regards to the position of their targets, but not close enough to deny the target a reaction (well, it is possible, just very unlikely).
Assume that PDs, external C3-related equipment, sensors and ECM, and heat-management components are at least in some regards exposed, i.e. not under armor. (I mean, how do you armor an antenna anyways?) With this, also regard the heat problem as solved as long as there are enough functional heat-management components.
Assume, for the purpose of this question, that ships will not run out of fuel by burning and maneuvering, however the inertia problem is not solved, specifically g-forces on human personnel and hardware (yes, assume that ships have a human crew).
How can I justify the use of both missiles and drones within a scenario like this, assuming the drones don't actually suicide?
Note: Why am I asking this question? It seems that there is little to no reason not to only use missiles and completely dismiss non-Intel/CounterIntel drones.
from the comments
You want a drone for any situation whereby multiple less powerful shots are more useful than one big bang. That said, in a space scenario where loitering is essentially "free" the line between a suicide(-ish) drone and a missile might be very blurred. Is a loitering missile with shields or anti-anti-missile munitions (which could be used in an anti-shipborne-anti-missile-projector role) really a missile or a drone? But the real question is, why would you have people in frontline warships when you have drones?
I think you misunderstand. I defined "Missile" as any self-propelled object whose primary objective is to detonate itself, the distinction to a "drone" is purely meant as a meta distinction to have a different word, to have a clear distinction between something that is clearly a one-use weapon and something that at least has a potential to be reused.
It's not necessary to have an all-purpose drone, I just want some justification of why there would be a need to have drones with point-defense like armament.
The role of humans in frontline warships is to make decisions, since there is no "near-almighty" AI and no realtime FTL communication. Drones have no FTL themselves, and the accuracy of catapult gates decreases with distance. Also, for story purposes it's nicer to have humans.