[Someone]

I would not use a rocket. If you can see or hear that drone, you can fly your own drone into it, or have it explode nearby it. Such a attacker drone would not need 20 hours endurance, so it would be a lot cheaper.

That "If you can see or hear that drone" probably is where the problem lies, but that might be solved by having your drone listen for the distinctive hum of the drone's engines. That way, you don't have to be able to continuously see that drone from the ground. Just launch your own drone; if it hears another drone, it will home in on it.

Alternatively, I would try jamming the drone's signals or taking over its controls.