+1 for looking into an inline fan after the duct merge. I am guessing that with all the joins etc the duct length will be quite long? If so a bit of additional draw that is switched on when either are used could help and prevent any flow the wrong way. Would have to check the wiring though as it would need to be linked to the wiring in 2 special locations, both should just be the lighting circuit though (but you may have two of those).
Or am I right in thinking that the cooker hood will be a centrifugal fan as that might prevent flow back better than a crappy axial like you get in a bathroom ceiling.