I have made a lot of dog coats for a lot of different breeds of dogs. In my experience, you need to shape the coat to the dog's back end with darts in order to keep it in place. Where the darts are placed and how many you need depends on the dog's shape. Sometimes one in the center back in the last third of the seam before the tail end is enough, although I usually use 2 on the sides as well about 2/3 of the way down. Maybe play around with a vest cut out of some throw away fabric to get it right before you try it on your vests.
Another way to keep it in place is with 2 straps crossed underneath the belly like you see on the Foggy Mountain dog coats.