It's probably not a good idea to limit your caloric intake if you are already experiencing fatigue symptoms. Just my opinion.

You are skirting around a lot of issues that will compound your chances of injury. Injury management is a huge part of endurance running. In reality, running 18 miles takes up a good 1800 calories, nevermind the rest of the day and chasing kids. You should take in the calories, chances are you might lose some weight anyway in a slower manner. But, not eating enough will increase cortisol levels which will further breakdown your body and subsequently your mindset. Hormones that induce hunger are going to drive you insane too.