If Emma bit you, you would be wise to get an anti-tetanus jab if you're not already well-protected.
As for frolicking in the waves, it raises the quasi-philosophical question as to what's more important, dogs or children? Our children are precious to us, we invest huge amounts of time, money, and emotion in bringing them up to be the future of humanity. Your dog is your hobby. I'd add to that that dogs do not routinely clean themselves or are cleaned by parents, unlike children, they carry several pathogens in their unclean mouths and up and around their unwiped and unwashed anuses. So no, dogs and children should not mix in the sea. In fact, dogs shouldn't even be on busy beaches at all.