Parvati, personally I agree with you about renting a car instead of depending on buses, subway or taxis for hauling kids around. Just so the OP knows, however, be prepared for some serious aggravation, and depending on confidence and driving skills, perhaps moments of brief terror
To me, the cabs are the worst for things like this. Hell, they won't even stop most of the time for someone with three bags of groceries, much less kids, car seats, etc. And hell, I've met very, very few compassionate cabbies here. They do exist, but few and far between.
Buses are difficult to get into, seems to me, with kids - you often have a line of people trying to pay the meter when you're getting on and it wouldn't be too easy trying to handle stroller, kids, etc, at the same time. Certainly can be done, but yuck.
I drive here, I have my own car. I've been driving here for about 5 years. I'm very comfortable doing so, but I've also driven all over the world, both on left and right side of the road, in conditions that freak a lot of people out. I'm a bit of an aggressive driver, which (as strange as it may seem) makes you less likely to have problems (as long as you are also a good driver and not just a calamity waiting to happen). People here who drive are completely oblivious to what is going on around them, make turns to the right from the left lane, and vice versa, without even looking, get caught in the middle of an intersection when the light turns red because they were trying to squeeze themselves into the next block before the light turns, etc. And wait until you are driving down Santa Fe around Plaza Italia and there are literally around 15 buses, all over, squeezing you between them. Buses are like big elephants that just don't care at all about any other vehicle on the road