I don't have a complete design ready, but I suggest using a NE-2 neon lamp with a 100k resistor as part of the input circuit. The reason is that ringing voltage is the only thing on a phone line that will trigger an NE-2, and if you use one, you'll be ensured of absolutely zero conduction (no leakage or load) when the phone isn't ringing.
You might even detect the triggering of the NE-2 photoelectrically. That will completely eliminate any questions of grounding between your telephone circuit and your other equipment.
From there, maybe a 555 monostable working a solid-state relay in the AC power line to your DSL router.
Or... Why not figure out why the router needs resetting frequently, and fix the problem?