I think it may have to involve you and partner eating that way and getting rid of ALL stuff out of the house.  If they are hungry they will then eat what is on offer. 

Sorry meant get rid of all temptation and all go on the same diet.  If stuff is not there in the first place, then they are going to be a lot easier to handle.  I would make low glycemic snacks and have those handy for them to eat instead.