DUS is the second largest airport in Germany. It has a good subway system, but I personally would not go downtown for a 7-hour layover. You don't know how long the security lines will be when you get back, or if there will be any delays. The river bank, TV tower, and the more interesting parts are not right at the HBF, so you need additional travel time (and buying Metro tickets at a machine you are unfamiliar with) for all those people. However, this reservation is a personal opinion. Will your luggage be checked through, or do you each have two air tickets?
I would think you want to visit the Altstadt, but we don't have the time of year or the time of day, or the day of the week. Are you landing at 7:00AM? There are also museums and plenty of restaurants in and near the Altstadt. Do all these kids have good walking legs? (In NYC where I'm from, everyone walks a lot. In NJ where I live now, not so much.) Will they be exhausted from poor sleeping on the plane?
The many Brewery restaurants in the Altstadt have great German food, but it's hard to eat in 59 minutes anywhere in Europe. No, they don't care that your children are underage.