Bring the Kid!
In one of those incidents that proves life really does require a sense of humor, I very unexpectedly became a father at the age of 51. My partner and I agreed that we didn't want to use any day care, so we are basically doing all the bringin' up of our son ourselves.
The practical upshot of this is that my son is often at the studio with me, and like any healthy and energetic toddler, he requires some space and games and toys to entertain himself while I teach.
Which means my studio is about as kid-friendly as it gets. I have a child-safetied play area stocked with toys and a DVD player and blankets and books and so forth. I have a basinet for infants, and a pack-and-play crib for toddlers. I have a dedicated dressing room for clients which can double as a nursing or changing room, and I am fully equipped with creams and wipes and all of the infrastructure a young kid requires.
So, by all means, bring your infant or (well-behaved) young child. Being the parent of a youngster should NOT keep you from your exercise. As one former client used to say: "The hours I spend here with you are all that keep me sane, in a world full of baby talk and dirty diapers!"
Note that the child will not be involved with the exercise (like a Mommie-and-Me yoga or music class), we'll just keep them occupied while you get your fitness on!