You woudl have to create two separate email calls (one for Part A and one for Part B). You could remove or hide Part A or B accordingly so that the user could not see it but be aware that it is still there in the form. Depending on how you do this you woudl have to turn off the mandatory fields before you hide the pages. This woudl all be done through script.
If you are not good with script I woul not suggest attempting this as a fair amount of code will be needed.
Paul