Wiring an e-stop with secondary reset
It's the latching circuit, that you require, which is the basis for relay logic.

The schematic shows how it's to be configured for the E-Stop function.



When the mechanical-latch-type E-Stop button is actuated, it de-energises the 'Control' relay and shuts down the machine.

When the E-Stop button is released, the machine remains  shut down till the 'Control On', 'Spindle Start' and 'Automatic Start' buttons are actuated with all starting preconditions fulfilled.

This safety feature is called 'Zero Volt' safety. When power fails, the machine shuts down and does not restart on restoration of power until it is commanded to. 

The manual E-Stop button is actuated when a danger is foreseen by the operator. Automatic E-Stop can be triggered when the 'NC' contacts of other fault tripping mechanisms are wired in series with the E-stop 'NC' contact.