Well, I hope you had an enjoyable time with your family at the parade! Fortunately, you did not have to have the conversation with your cousin. If this comes up again, I would keep it very simple if this works for you. Being that you expressed your wishes on a previous visit and they were disregarded, I would say no to the dog, stating that it will not work for you and hopefully you would not be pressed further. And if pressed, remember the mantra, "I'm sorry, having the dog in my home will not work for me." And then perhaps you could suggest that she board the dog or have a neighbor watch him.
I have no children, however, I can understand how easy it is to turn a deaf ear to them. I have many siblings and when we were young they could be very unruly and I would pay them no heed.
Some parents allow their children to run wild, without any consideration as to how they are impacting the people around them. Personally, I find this very annoying, I truly appreciate parents that are considerate of others, obviously your cousin is not.
I don't know what would work with the food and drink situation. We have a home that we now rent out, we moved from the area for work and are planning to return for retirement. Recently I showed it to a family interested in renting it and found myself aghast! The parents were lovely people, they brought their daughter and her friend. The girls were running through the house, banging doors and drawers and the parents did nothing! It was a very uncomfortable situation, I asked the girls to please stop with the banging. I think if the parents do not step in, you have to speak directly with the children. The girls stopped, but it wasn't great.
So the language I like to use:
.......does not work for me
I would prefer if you do not........
It is possible to keep it honest and polite, just keep it very simple.