1 if it is a Trident the breaker will trip if you ask it to supply two solenoids.
2 IMHO you need 2 seperate systems as you are likely to be running the heater at different times to the cooker.
Excuse my lack of knowledge but is trident a type of breaker or the way it is wired. And I think I will be running 2 seperate systems. Thank you for your HO!!