I do a lot of co-op by myself. Me and my mule. Lol. There are a few points in the game where they forcibly require you to be with your teammate. Second time was the Wildlife Exploitation Preserve mission, when you deal with the boss. There is a way to get your mule closer to the final destination by entering and exiting the Natural Selection Annex. From there, your mule needs to run very fast to get to the final elevator. Not easy with a mule that can be 20 or more levels less than the campaign requires.
To fight Tinder Snowflake, your teammate needs to be present to ring the bell. The fight with Hector in the Commander Lilith DLC will also suck the teammate into the battle. Same with the Leviathan, afaik. When I died to that beast, the mule had to valiantly fight the boss. Another nasty example is the fight against the handsome dragon. You have to drag your mule from one end of the map to the fight. If he is not with you, then he does not make the required checkpoint. Also the Tiny Tina DLC requires all teammates to be present to start a round in Murderlin’s temple.
Overall, however, there are a lot of missions where the game allows you a free pass when you carry a mule. The fight with the Handsome sorcerer can be done with a mule parked near the fast travel station.