Safety Relay Circuit
As you think through the logic of how this would work do consider the possibility that the power can go off and put things into a state that needs to be safe. One way to deal with this is to allow the system to disarm itself when the power goes off.

I could envision a system where the E-Stop switch cuts off power completely when the switch is in its pushed in state. When the E-Stop is twisted so it pops back up it would reconnect the main power connections. It is a good practice to use a double pole switch for the E-Stop so that both sides of the AC mains are cut off by the E-Stop switch.

An arming button (or reset button as you call it) would be a momentary switch that activates the coil to an arming relay that is wired up in a way to latch the relay on through a set of NO contacts. This relay's latched behavior ceases when the E-Stop switch cuts off the power or there has been a power loss. This arming relay coil is best if powered from the mains power as supplied through the E-Stop switch. Some applications like to use a power supply to run the arming relay from a lower voltage but the holdup time of the power supply can cause this relay to not unlatch when there is a momentary AC mains power loss.

The arming relay in turn activates your main power relay to allow power to go to your motors. A pair of NO contacts on the arming relay are used for this purpose and the main power relay coil may powered from either AC mains or some other power supply derived voltage source. The NO contacts on this main power relay can be used to switch power into the motor controller or could be used to switch the motor controller output leads to the motor itself. This choice of how to wire this part is dependent on the types of motors involved and how the motor is being controlled.

There are additional considerations that should be taken into consideration in designing a safety interlock system. Sometimes redundant relays are used in series if there is a possibility that relay contacts can weld together thus preventing circuit disconnect. 

The idea presented here is intended to use a relatively low power relay for the arming relay and using that to create the latching action. Lower current switching can make this more reliable as opposed to trying to create the latching function on the main power relay itself.