Mabel,
I would get some other recommendations also. I know if I was just expected to drop Cody off with some stranger, I would not feel comfortable with that at all - They should have at least a two way mirror, so you can see what is going on and I would think the trainer would be working with all three of you since you two are the ones relating to Milo on a daily basis.
Speaking of Cesear though, I know from watching the show, that he also works with the people, but don't people send their dogs to his place for 2 or more weeks at a time? - at least the show portrays that in cases where dogs are fearful of other dogs.
Mabel, what else does this trainer do? - you said he works for your vet? you mean training animals or in some other capacity?
You need to call them and get more information if you are considering them. I know you posted that it was your fiance that talked with him, but I myself would do the calling(men can't always hear correctly
)sorry, didn't mean to insult anyone, I am just speaking from experience.
In the meantime, if I were you, I would still look around into other behavior training places.