yes a vet will usually give a sedative for a flight if you ask for it.
I play fetch and tug with the same toy and I have never had a problem with it. Not sure why that would be a bad thing to do. Lily has a good "drop it" response but I am not sure if I gave her a treat and told her to drop it she would. I think it would be confusing to her if I gave her a treat then told her she couldnt have it.
I got Lily to learn "drop it" just by playing fetch with her and when she would hold on to the toy I would tell her drop it and give lots of praise when she did.