If you are hoping to get your kids into a wholesome sport through the nasty teens, then think about what the high school and collegiate teams are using. Go to
CollegeSailing.org - Inter-Collegiate Sailing Association of North America (ICSA) to get a good feel for what's going on in the world of youth sailing. There are also tons of sailing camps.
I grew up sailing the Flying Junior, commonly known as the FJ (which was acquired by Vanguard). I'd be shocked if you couldn't find a 70's vintage for $500. I'd argue that you should get a boat that has a head sail, and a little length (like the FJ), as the three of you can go out together. You drive, one tends to main and the other to jib. Everyone has a job and a purpose (like on a race boat). As they begin to understand that job, rotate everyone to new positions.
I've also spent (and still do) a considerable amount of time on Laser's. Because of the age of your kids, I would not recommend the Laser, as it would not fit you and your two children. It's actually a very difficult boat to sail when the wind picks up. Cramped quarters and lots of capsizing leads to crabby kids!
Other options are the Sun Fish or El Toro. Both are great options if you want to sit on the dock and watch them sail, or do a sail with you and one other. Again, shocked if you couldn't find one for $500.
btw, I started sailing when I was knee high to a grasshopper and I've always thanked my Dad for getting me out there at a very young age. My kids (7 and 5) love it, love it, love it. Look first around your area to see if there are any youth sailing groups, as you may be able to join a club for way less than $500, and have access to great boats and great people you and your kids can learn from.