To be honest in my opinion you need either a break or a new job.

How would you feel if your parents or family left you in a strange place for a while? I'm sure you would be frightened too, We cant communicate with dogs like people do so they dont really have a clue what is happening to them! In my opinion its part of your job to comfort a scared dog not to just leave it in a cage and still charge for a walk as you said, Dogs react differently in different situations, They have a stranger walking them in a strange place I would expect at least a bit of playing up from them because its a totally new experience to them.. Do you always feel like this? I would seriously consider a change in jobs because it sounds like you dont have much give when it comes to them. Maybe the owners are trying to make your job easier? I think I would prefer to have a baged meal for the dog instead of having to measure them out making more work for myself, I very much doubt they want to make you look like an idiot I would assume it's to try and make your job easier for you.

Are you under alot of pressure at work? I think you should talk to your boss or superviser to try and sort something out