Q. How can I keep my 14 year old Yorkie from snapping at the younger ones?
A. It's all about management. Do not allow the 7yo's to interact with your 14yo unsupervised. You should be there each time they interact so you can redirect the 14yo's attention onto some toys, or onto some treats when the 7yo's are around. It sounds like you need to help your 14yo make positive associations with being around the younger pups. You should be trying to feed him treats each time he interacts with them, and doesn't snap at them. Pet and praise him each time he is around them, or any time they are near. As I said, keep the separated when you cannot supervise their interactions because if you aren't around when he is snapping at them, you could end up with a fight on your hands.
It could also be that they spend too much time together. Imagine spending 100% of your time with somebody, day in and out, doing everything together... including going to the bathroom.. that might bother anybody. I think you should give them more time apart from each other. Take them all on separate walks, separate them to play with them individually, separate them when you take them to potty, separate feeding times in separate rooms, etc. This can help alleviate the stress your older dog is feeling due to living closely with other dogs. You should always be giving individual activities in a houseful of dogs anyway.. when you expect them to get along 100% of the time, that's when you find trouble.