I agree that April vacation may be your best bet, if that's when your break is. Avoid the time around Easter. (Though, I've known people who went the first week of April when Easter fell then and said the crowds weren't nearly as bad as they expected). Taking a 5 year old out of school isn't usually a big deal - though it is in some states. But taking a 15 year old can easily be a big deal. You can also look for smaller school breaks so your children don't miss as much. For example, in-service days or other things that give you a 4 day weekend. Then your kids won't miss nearly as much.
As for time of year without considering school, I would stay away from Sept since you don't like the heat. We went the first two weeks of Sept of 2014 and it was brutal - as in heat indexes over 100 sometimes! I live in the southeast and we still struggled with the heat. We usually go in Nov/Dec, avoiding the holiday weeks. The crowds have always been quite manageable then and the weather great. The crowds are moderate, instead of low, but still easy to deal with when the weather is nice. Dealing with the weather is harder to do than dealing with crowds IMO. We did the last week of January one year and it was record lows and so incredibly cold. It was too cold to swim and even super cold in the parks. The crowds were very light though.