M.R.
To me Curves seems like a colossal ripoff, selling the concept of "hey it's more comfortable in here because we cater to larger women" but at astronomical fees. You may be better off going to a place like Cardinal Fitness, which is one of the less expensive places. I'm a member at Cardinal Fitness because I just need a few cardio choices and all the cybex/free weight options available. I don't need a pool, spa, tanning, classes, rock climbing wall, or all the other frills that come with the more pricy clubs (although if you're into that and want to explore it, a club would be a great place to start!). Cardinal also has a Kids' Club to watch your kid while you workout. Cardinal is $19.99 a month for a single membership (there is a $99 initiation fee), and you can discontinue your membership at any time provided you give 30 days notice.
Keep going to Curves for your 30 days, learn about the machines and write down your workout. Take that with you to your new place. If I am remembering correctly, the '30 seconds' workout you're describing is actually a great way to 'circuit train' without eating up a lot of time. In this case, circuit training means you move through each of the weight training exercises quickly with little or no rest in between. You still are providing adequate resistance for your muscles to tone them, but because you are not resting as long in between sets, you are not allowing your heart rate to drop, also making this a good cardiovascular workout.
As far as childcare goes, I agree with a previous poster about being wary of taking a child under the age of 3 to any health club childcare room.
If you're interested in finding more about workouts, www.sparkpeople.com has some great ones.