OK, now that Jim and I have sold you on DHP, a couple of things you should probably be aware of if you're not already:
1) The hookups are electric only, 20/30/50 amp. We had no problems with the electrical. There are NOT, however, any water hookups and the bathrooms do not have showers. There is a dump station but no place to fill up with potable water, so you have to fill your water tank before you get to DHP. I think we stayed two nights and didn't have any problems with our family of 5, but we definitely tried to conserve water as much as possible. With a family, I don't think I'd want to stay longer than 3 nights.
2) The size of the sites varies greatly. Take a look at a satellite photo to get a feel for which sites would work best for you. Small campers are definitely better. We have a 36' RV and there are only 2-3 sites that would work for us. Many of the sites are not very level, particularly front to back. I found the sites on the east side, outside of the loop to be nicest, as they are elevated a bit and have a nice view of the setting sun. You can also see photos of all the sites at http://www.campsitephotos.com/campground/Dead-Horse-Point-State-Park . Depending on the size of your group, you may be able to share one site, because each site has its own tent pad, as well as the site for the RV. I looked at the reservations website and April is already largely booked up. I recommend calling the reservation line now, to find out for sure the earliest date you can reserve your desired dates in June. When I reserved last year, it seems like the website explained it better than it does now.
3) Keep a close eye on your kids. There are great trails that leave right from the campground, but within a quarter mile, they come to 500+ foot sheer cliffs. No rails, no signs, etc. Stunningly beautiful, but if you have kids that won't obey instruction to stay with you, or are prone to daredevil behavior, it could be a scary place.
With all that said, DHP was our favorite campground for our entire two week trip to Utah. Good luck and let us know how it works out.