Your post is quite confusing tbh so it’s a bit difficult to say who’s being unreasonable.
So once you arrived, you had a stroll, river swim and starters with your friends? It sounds like they spent a decent amount of time with you then, not just went off in a huff?
Were you just finishing starters at 5.30 (when they had to leave)? Was the meal you were meeting for meant to be lunch or dinner? That seems very late for lunch.
What does ‘they hadn’t realised this place was a fave restaurant and close to their home’ mean? I don’t understand their justification for needing to go to a different restaurant. If it’s a favourite restaurant of theirs, surely they know where it is?
I’d guess they probably feel you should have planned ahead for traffic, since it’s a Saturday in August, and felt it was inconsiderate that you didn’t and kept them waiting instead. How old is your DD, re needing to pee? Maybe it’s because I’m not a dog owner, but I don’t know if I’d be hugely impressed if I was waiting for late friends and they texted me that they’d stopped the car to give the dog a walk. Again, seems like things that should have been budgeted for and you should have left earlier to accommodate them. I don’t personally consider 40 mins a huge amount of time to wait, but if I felt I was waiting because my friends had been disorganised rather than because there was a genuine issue that couldn’t have been predicted, then yeah, I’d be annoyed.
ETA: I’ve just seen your peeing DD is a teenager, not a small child. Yeah, YABU.