Yes since we love your kids. If you bring them great but if you wouldn't that's also great we want our wedding night to be a night off for you. Either way they will have a good night.
If your invitation says “and Guest,” then yes, if not, we would prefer if it was just you.
Cocktail, please. But we want you to feel comfortable, so if those shoes are too high or that top button is too tight, let it all hang loose.