We will see on the leash issue. It may come with time and practice, and it may be that you feel more comfortable with her on lead and so that is how you will work! Both are ok. No one right or wrong way and the environment or situation may dictate how you work. Personally, when truffle hunting myself, I do both, sometimes even during the same session depending on the dog I am working with and what feels appropriate for that day and time and place.
As for truffle transportation and samples taking them to sites:
Since you are using frozen- if you’ll only be gone and out for a matter of say 3 hours, yes that is ok BUT:
It is going to be HOT in your car where you are this time of year so that will cause your pieces to decay faster. Luckily frozen aestivum holds up better than most species for this, so you can get away with more. But yes, absolutely double bag it (so odor doesn’t permeate everything in your car!) It isn’t the fact that the piece is unfrozen that is problematic, it is the process of decay. But like I said, Aestivum holds up fairly well to this.
When we transport truffles (usually larger amounts of fresh/ frozen) we use a small cooler with ice packs. Another thing I have used in the past is a small chilled bento box type container that kept the samples cool for upto about 6 hours when training, even just left in the car. Everything helps in terms of decay.