Do dogs get diarrhea due to stress?

Yes it is very possible that the diarrhea is due to stress. Dogs are a lot like people in that respect. If your dog has not had a lot of socializing with other dogs in the past I'm sure he was nervous. I would continue to take him to doggie day care once or twice a week so he can get used to it and other dogs. He will get more confident each time and by the third or fourth visit he will be pulling you to get inside but he will be just as happy to go home with you when you return. It is a great outlet for the dog and gives them mental stimulation.