N.L.
Consistency is the key. Are your children sleeping through the night? This is important so do what you have to do to train them to do so. There are plenty of books and advice on how.
Next is your consistency. It doesn't matter if it is 6 hours, 9 or 5. If your body is consistently (even weekends) on the same schedule... to bed at 11pm and up at 5 am, then your body will adjust to the sleep and it will be enough. You should also be sure you are drinking a gallon of water a day. And also, you work for the city? great, that means you get benefits such as scheduled break times. If you get an hour break, try instead to request a 30 minute lunch and (2) 15 minute breaks or (1) 30 minute break in the afternoon. Or you take the 2nd half of your lunch break and guess what, you sleep! Don't get into all about how you can't really sleep and there is no place. Get into your car if you have to, or ask a friend to borrow theirs for a nap or lock yourself in an office. Even if you don't fall into a "real" sleep, just closing your eyes for 15 mins and shutting down will be extremely re-energizing. You set your cell phone alarm so that you don't go over, and you nap. All of us get tired mid-afternoon b/c it's the time that the brain releases a certain hormone that triggers need for sleep. I forget the exact number, but it's something like 8 hours after you wake up that this hormone is released.
Anyway, good luck and try it all girl. You gotta get your body to feel better or it will adversely affect your health, possibly even long-term. Make it happen- you're single mother, mover and shaker to get it all done so add this to your list. Go girl! N.