cops101. there aren't (known) pharmacokinetic drug interactions that would advise you to avoid taking Tymlos at the same time as your other medications. I like your plan to take the injection a half hour before exercise. It will give you time to ascertain that you aren't feeling likely to fall. And just might give you a little extra energy for the workout.
I'd take a small bag for the tiny sharps and probably at most the single pen you'll need to dispose of in a four week trip at a fire station or pharmacy.
I travel with small ice packs because I'm on Forteo the one without preservative. But there are fancy thermoses you can find on amazon.
You are most probably having bone markers to make certain the medication is effective for you, You are suspected of having a very good doc,
Returning your good cheer,