Giving anyone melatonin is not good, especially for a toddler. The body will get out of balance and may grow to be dependant on it.
Calcium/magnesium supplements help calm the body. May seem "out there", but this acutally helps children/adults who are adhd. Of course she can't swallow yet so two things: find a reliable company who makes a high quality calcium magnesium supplement (so there isn't any contaminants) and secondly find one that is chewable and doesn't contain a lot of sugar, which would offset the positive affects of the magnesium.
So icalcium will help her bones and the magnesium calms the nerves and muscles.
What about soothing music for her to listen to? Or maybe one of the coloring books where the markers only work on that type of paper (can't think of the name).
Also, it sounds like she is a high energy child and may not want to sit for any length of time.
One last thing...Have you tried to travel at the times it is her nap time?
Good luck and safe travelling.