S.M.
(rant alert!) Good judgement call on your part to avoid those dojos like the plague. No martial arts school ought to be making any requirements like that for any kid, much less such an extremely young one. Even as an adult, I wouldn't become a member of a dojo that stipulates some mandatory time obligation. (My husband, son, & I currently take Aikido.) I mean, I've got kids to worry about, a job to worry about, friggin' mountains of laundry, various family obligations, muffins to bake for school festivals, volunteering at the school, etc etc - the last thing I need is MORE stress and guilt from my hobby! My family is there for enrichment and RELIEF from stress, not for yet another group to make further demands on my time, and the same goes for kids.
So one tip in selecting a martial arts school (or dojo) is look for one with NO CONTRACTS. Those tend to be more commercially-oriented, and what you want is people who are just passionate about their art. Choose a dojo with the same care that one would in choosing a church, because if you're lucky, your child (and maybe you, if you get hooked) will be putting a lot of heart and soul into it. If most of the sensais (teachers) have a profession outside the dojo, that's also a good sign. (They have a job to earn a living, and the martial arts they do for love.) Strip malls seem to be magnets for very commercially-oriented dojos, but I wouldn't rule on out completely just because it's in a strip mall. You gotta find one with a good spirit.
If you can't figure out whether they have contracts or what their rates are by looking at their website, or they only say something like "your first (class/week) is FREE!" I wouldn't even bother calling them, personally.
It's also a good sign when they offer a flat rate - one price and you go as often as you like. (Of course, then you have the financial incentive to go more frequently. But that's only a bad thing if you're trying juggle too much, which you probably are right now, but I understand how kids like to try things out.)
I don't know of anything in your area, but I'll send you some links to a few dojos that I'm familiar with so you can get an idea of what to look for. (Keep in mind, the two places I'm recommending don't start kids classes until age 5, which in my opinion us another good sign, because they figure that kids under 5 just won't get much out of it.)
http://www.roswellbudokan.com/ (Our 2nd home - note how easy it is to find the pricing.)
http://www.cuongnhuatlanta.com/dojo.htm
Lastly, here's a good quote I read recently from a different Aikido group in Atlanta - from "How to Find a school":
"One of the great secrets in the martial arts is that there are people, and schools who practice because it is something they love to do. They are usually smaller in attendance, allowing for a more personal teacher/student, artist/apprentice relationship which is how martial arts have traditionally been taught. On top of smaller classes, many times these school charge less than more commercially oriented schools. But they can be harder to find, since they don't always have that big sign on the freeway." -Larry Feldman, http://www.atlantaaikido.com/rants.htm