If I understand what you are describing, you will not be able to do this using an alesis realhat pedal or DM10. You could, in theory put multiple components together to get what you are after.
First, let me clarify something - I have not seen a e-hihat with edge/bow/bell zones. It's typically bow/bell only for a designed hihat. There are other cymbals that might give you edge/bow, or edge&bow/bell, but not all three - unless you used a 3 zone ride cut down.
Having said that, you would need a secondary hihat pedal or switch and a trigger i/o, or possibly another module to do what you need. The DM10 would control the edge/bow hat (open/closed) and the trigger i/o would have the secondary pedal or switch for the bell.
It may be possible to mechanically connect the pedals, or possibly install a switch underneath the hihat pedal, so when you press the pedal down, it closes the switch. This would require a momentary switch - releasing the pedal releases the switch. Otherwise, you would have to press the pedal down again to trigger the switch again.
From what I can tell, you are looking to get 4 different sounds from your hihat, depending on the zone and pedal position.