Capturing the Audio
Because the iPhone only has a nondirectional microphone, it can be very hard to capture good audio of children, who tend to have softer voices (well, obviously not always) and converge in noisy places. If audio is important to the scene you're shooting, get close to your subject, incorporating whatever framing adjustments are necessary to do so. Ideally, you'll be able to shoot important audio in a quiet area, which may require some moving—or some requests—on your part.
If you regularly shoot video of your kids where you want better audio than the iPhone can provide (I'm picturing settings such as gymnastics class or the playground), consider getting a higher-quality microphone and an iPhone adapter that allows you to plug in the microphone to use with the video camera. While microphones are available in a huge range of styles and prices, the adapters are inexpensive, and having a separate microphone can improve your recording capabilities immensely.