I have always been told:
If the dog has diarrhea, do not feed for the first
24 hours and than the next day feed a little
food and rice.
IF the diarrhea lasts longer than
2-3 days or if their is fever or other sick symptoms present
than take to the vet ASAP.
Changing dog food could possible be the problem too.
When changing foods you need to gradually add the new
with the old. Like you, I also bring our dogs food on our
vacations.
I probably bring to much food now.
After one of our vacations
we were running low, I made my husband drive around
till we found a feed store that carried the brand of
dog food we use. lol
If you are looking for a supermarket food, I heard
Purina One is a good food.
I do not know if they make a puppy food.

Hope your puppy is feeling better very soon. : (