I have 2 pups 9 and 10 months old. When I feed them in the morning they keep changing their feed dishes. Then one will vomit. I tried puting them in different rooms to feed, but then they cry and won't eat. Both have been wormed. I thought one was getting to much food at one time so I cut the amount in half but worry they are not getting enough. They don't vomit at the evening meal. Both have been to the vet, she found nothing wrong.
Do you have a crate to keep them in that you can feed one in, and not the other, so they can be in the same room eating but just not able to reach each other's food dish?
To me, it makes no difference if they cry or not. It's your routine they need to follow. Put the food down for them when you want to eat, give them each 20 minutes to eat. If they dont' eat in that time, pick up the dish and wait until next feeding time.
My Mom's cat was having the vomit issue, couldn't find anything wrong either. She then was advised to raise the feeders up to chest level or even a little higher and suddenly it stopped. I have all of my feeders about that high and no trouble. Just maybe worth a try.