I did something similar, only in the reverse direction. I was in the MD program and applied to vet school. I applied after first year medical school, second year medical school, and after graduating from medical school (with Distinction), and could not get an interview for the DVM program. This was because my marks for the DVM prerequisites were sub-par. It didn't seem to matter that my subsequent course-work both before I got into med school and throughout med school showed very good marks ... the vet college I was trying to get into (based on Canadian residency criteria for the various vet schools at that time) only used a specific formula for marks and I could not compete with those students who had always been "straight A" students.
Finally, after I had finished a couple of years of post-grad medical training (residency), my residency status changed based on where I was living at that time and I could apply to a different Canadian vet school that had different admission criteria. I won't bore you with the gory details, but I was finally granted admission in 1999. I had to fulfill the same admission criteria that were required of other students despite having an MD behind my name. And, I had to do all of the coursework in the DVM curriculum. Actually, I was told that I'd get credit for first-year physiology & something else, but it was only a class or two and they were at different times so it didn't even give me a morning off or anything, so I just did the coursework as a review.
The comment from the other poster about proving that you are not going to "bail" from med school because you are applying out of vet school ... this never came up for me, at all. Certainly I was asked why I wanted to go to vet school when I'm already an MD, but it wasn't asked in the spirit of "why are you bailing". It was more along the lines of, "what makes you tick". For what it's worth, I didn't bail on either professional degree. I'm practicing both as a physician and a veterinarian now and have been since 2006.