As this isn't a normal situation I wouldn't treat their eating style/habits as normal either. They could very well be full and then be hungry again 30 minutes later. Perhaps they have a sensitive stomach which causes the vomiting after too much food but they still digest at the same rate and if they have only eaten a little bit then of course that would be through their system quicker than others and they will be hungry again sooner. Some people can only cope with eating very small amounts but more frequently. I wouldn't worry to much on the why it happens and concentrate just on finding a solution but don't have an expectation of them that is comparative to any of your other children regardless of age. The goal is to stop the vomiting and if they complain they are hungry shortly after a meal then you need to tell them to stop asking and that when it is snack time they will get more food. if you absolutely must then just give them half a piece of fruit that they can eat easily without disrupting the group or current activity. They are 4 and 6 and need to be told and they will have to learn that this is how things work in your house. Very very slowly introduce an extra bite of food after you have had a 2-4 week period of no vomiting and see how this works. Also tell the 6 year old for sure that if he feels sick to run to the toilet!