Children can be finicky eaters for sure, but Dubai's eclectic food culture can please even the most fastidious of palates. Malls in Dubai are great because they have such large food courts with a multitude of options. Get to choose either from fast food, healthier options, or ethnic cuisine such as Lebanese, Indian, or Chinese among many others. Malls have fast-casual dining alternatives as well, and these are specifically suited for families.
Most of the best restaurants in Dubai are in hotels, and nearly all will have a children's menu and will be glad to accommodate any special requests for special dishes or modifications. Atlantis, The Palm is a great place to explore during meal times, of course, the sheer number can leave you overwhelmed, which is a different problem altogether!