Help with relay wiring

I'm going to suggest that you leave the circuit exactly as it is. The circuit as designed, is protecting the reed switch. The reed switch is not intended to take any sizeable amount of current, so that's the reason for the second set of contacts. The reed switch only has to pick up the one relay coil and nothing else, which seals itself in and closes the other set of contacts that will do the work. By sealing the relay, the reed switch contacts are shorted out and not carrying any current. The relay contacts take all the current to keep the relay energized.
From this design, there is no method to reset this circuit. Once the reed switch closes the sets the relay, the relay is energized until the main power is removed.