If you are driving (rather than flying) most of the time, you will have more control over your time. You will also be able to take some basic workout items with you (bands, a yoga mat, a few dumbbells etc.).
Combine that with pushups, pull-ups, sit-ups and crunches, leg squats and calf raises (with the dumbbells) and you can get in a solid workout just about anywhere. Think higher reps, lower weights. Granted, you won’t max out on the legs but you probably won’t want to during the tournaments anyway.
I’ll say that after being at a few out of town tournaments, working out is much easier said than done. It’s ambitious. It never ceases to amaze me how much time gets filled driving to the fields early, warming up pre-game, rain delays, normal game time delays, playing double headers etc. There will also be a game or a player he will want to see play. There’s hanging out with teammates.
For us, eating, hydrating, and recovery are key while on the road but my son is a catcher primarily. There are plenty of days where the game is the workout 
.
Good luck 3and2.