Cant see that two vets would knowingly want to treat an animal knowing it may be treated elsewhere as they wouldnt know what medication was being given.
My dog has her normal vet in Manchester and another one in Glasgow where she stays with my son when I go away. My son has full details of her medical history and the Glaswegian vet can always ring the Manchester one if anything needs clarifying.
I had a cat in London who was registered down the road, then the cat went to live in devon with my mum for a couple of years and was registered there. She was still with the one in London. Then mum and the cat moved back to live near me and the cat goes back to the original vets. Didn`t seem to be a problem. In fact when the cat originally lived with me I shared her with my neighbour who registered her at another place so she was with three!
If it's because the animal is in a different location on a regular basis - great idea providing both vet's are aware and have access to medical history. If it's because you don't trust one vet - just change - why the question?