...if these two planets are not even in the same system...
...presumably capable of crossing interstellar distances in a somewhat reasonable time... some VERY IMPRESSIVE thrusters...
That completely absurd.
Do you have any idea the amount of energy you'd need to move anything an interstellar distance? The sheer impossibility of getting from star to star in anything less than hundreds of years? The spacecraft would be
huge. Even allowing for advanced electrical propulsion(500 GJ/kilogram), your 100,000,000 kilo ship will need 90,000,000,000 kilos of propellant to reach .10c. I dont think that's accounting for relativistic effects. No, interstellar wars are impossible.
Taking your hundred million kilo ship again. To execute the dodge you suggested, it would expend 196 kilos of propellant(assuming again, hypothetical electric propulsion). Suddenly 100,000,000 kilos is 99,999,804 kilos. So we must question how much of the ship is fuel? What is the maneuvering capability of this ship? If the ship wanted to reach the sun's closest neighbor(not allowing for any sort of braking maneuver, just to pass by) in 45 years with a starting mass of 100,000,000 kilos, only 10,000 kilos or so are going to make it to the next star.
tl;dr
You hundred thousand ton spacecraft launches towards Alpha Centauri at 10% of light speed. When it arrives 45 years later it is still traveling at 10% of light speed but is out of fuel. It masses at about ten tons, roughly the equivalent of two Apollo Command Modules.
About the amount of rocks needed to make a hit:
You don't need to fill the maneuver radius completely.One can leave all the gaps they want so long as no gap exceeds the size of the target(allowing a modest margin for the destruction of incoming projectiles and the spacecraft's ability to quickly dodge into gaps and target incoming).Plus, one need not fire just one volley. I think it would be interesting to calculate how long a body like, oh say, the Moon could keep up that kind of defense before the lost mass began to effecting it's relationship with the Earth.
If you can see my cold rocks then I can see your warm troop transports. Hiding from thermal signatures against a 3 kelvin background doesn't seem very plausible. Supposedly, off-the-shelf(current technology) sensors could detect the space shuttle's heat signature from Pluto.
Or perhaps we have colonists arriving at mars whom, for whatever reason, are not welcomed by the current settlers. How would they fight in that case?
I like this one though, realistic. Though local martians would probably want the manual labor, assuming they were unhappy, I'd say:
Rovers filled with seismic survey charges parked in front of important buildings, snipers, sabotage, biological warfare. Knife attacks, sticks, stones, whatever they found handy. Crude landmines in well traveled areas.
Now that would make an interesting movie. An insurgency of Martian born settlers who think the new arrivals are there to steal their destiny.
But as for the asteroids, only Ceres and a few others have the sort of mass you'd want in a combat situation. I'm sure any disputes could be easily settled by calculating the amount of mass both parties had on hand and would be able to throw and simply declaring a victor without getting the universe all entropic. I think if the belt is independent(good luck with that), then Ceres would be master. Who ever held that would have the biggest rock and the deepest foxhole.