The honest truth is it makes no difference. The kids and dogs will be onboard (gee, I _like_ that word.. ;-) no matter what the pilots think. The biggest problems I see come from a skitterish dog/cat or parents wanting to mount their kids car seat in the rear facing seats. Note: generally speaking, the larger the child, the more the need to have them facing forward. Same thing in as in a car. The PIC tries to tell the parents what the safe procedure is (seat mounting, strapping down the pet cause of turbulence, etc..) and the parent/owner gets upset cause they don't like what the PIC is telling them. That's the only problem I've seen....
That said, I'm glad to see folks like NJAOwner noticing when we put an extra effort into seeing to the kids. As a grandfather of 5 young ones, I FULLY understand how important it is to occupy and amuse the younger children during a flight.
I always notice when we may have young kids coming onboard. [

] When I first get an airplane, one of the things I make sure of is that we have some fairly new and good children's movies onboard. When such a situation comes up, I preload one or more of the movies just for them. I make it a point to make the briefing as much fun and funny as I can and I do include the kids. In fact, I talk to them first, with the parents permission of course, and see what they would like to watch. I help to get their tv's setup, the headsets wired and turned on, and the movies plugged in. And I don't show them the sweets!
See, I grew up with a half dozen siblings riding in a station wagon all across the country on vacations. I know what the inside of an SUV, van, or airplane can look and sound like with a handful of bored kids. And I know what the parents are like afterwards... I take it as my job to take care of not only the kids during the flight, but to see to it that their parents... my owners... are just as relaxed and happy as those kids when they step off the bird.
Not all of my brothers and sisters are like this. I wish we all could be, but it isn't so. Experience has taught me these lessons and I'm trying to pass them on. Many of my fellow pilots haven't had the pleasure of dealing with several small children at once yet. It's not their fault they don't understand.... it's just social experience. So, don't be afraid to say something or mention this to the person you fly with. It will help.