Your offering up very confusing drawings here mate.!! . . . Your last drawing was ok just didn't need a Stop button.?

It's easy really just run 24V thru relay NO contact and then back to relay coil Positive. Then run wire thru Momentery Button(reset) between 24V and Coil positive. You can then run E-stop either in series with positive or Negative wire.
Latch will be made when Momentery reset buttons is pressed and dropped when E-stop is pressed and won't latch again untill e-stop is cleared and Reset button pressed.

Second contact on the Relay can turn on your Contactor. You can also use Another contact to pass Input (+) thru and back to Input (-) to inform software E-stop as happened.!