You need to trust your environment while meditating
A thought occurred to me last night as I was meditating, and it's very simple: You have to be able to trust your environment when you're meditating, or you won't be able to get into a deep meditative state.
For instance, last night as I was meditating (similar to the meditation we used to do in the corpse pose at the end of a yoga class), there were noises in the parking lot, neighbors were slamming doors to their apartments, and there was some yelling here and there. With that much noise around, it's usually hard to get my body to relax enough to go as deep as I want to. But, the one positive thing about my current living space is that I am on the second floor, so I don't worry about someone breaking in while I'm trying to meditate. If anyone is going to break into my apartment, they're going to have to come in the front door, and that's not going to happen easily, so that's what I keep telling myself: They can make all the noise they want, but until I hear gunfire, there's nothing to really worry about. This helps me relax more, and I've been very happy with the deepness of my meditative states the last few nights.
For anyone trying to meditate deeply in a loud, active family, or if you're a parent with children, I'm not sure what to tell you. The best idea that comes to mind is to find a good yoga instructor with a small practice, and pay attention during your poses, and really get into the meditative state of the corpse pose at the end of class. If you can set up a quiet space to meditate at home while your partner watches the kids, great, if not, well, er, good luck.