Guys,
Sarguy stated pretty clearly he doesn't want a trailer, and I looked up the Mazda5 and the website says, pretty plainly, "no towing."
I don't think there are even any decent hardpoints to be had for adding a hitch, and though I'm certain it wouldn't be difficult to add some, it doesn't feel to me like he wants to do something as irreversible as that.
The whole point I'm getting here is you're trying to put the luggage still on the car, but leave room inside for dogs, right?
Awesome dogs, by the way. The picture of the little one at the top of the thread actually wrangled a "D'AWWww!" out of me, which isn't easy.
Your points about the trailer are right on. In my area enforcement on the registration and lights is spotty, where it exists at all, but I'm right there with you about the registration and lights. It would drive me bonkers, no lights die like trailer lights in my experience, and every once in a while you find a LEO who just cannot let them go by.