Is there anyone who can help with some of the responsibilities during the week?
You mention your house is a wreck - are you in a financial position to be able to have a cleaning service come in once/month to help? I personally don't use one, but my obligations are full-time employee, mom to 2 kids under 4 and a husband (plus family pets). I don't have school, MIL to take care of, etc., but we have no family nearby, so we're always with our kids and have to accommodate everything we do because of needing to care for them.
Would your kids understand if you were to have someone else take them to practice once/week? Could you arrange a car pool with some of the other kids on their team so everyone helps out equally?
I didn't think I had time to work out either. I am the kind of person who goes into everything head first. My husband started training for a 1/2 marathon last year, and I was committed to doing it, too. We both ran it last weekend, and finding the time to train was tough, but we did it. We had to alternate training days and times. Initially, we'd set the kids-up with a movie in the basement, and one of us would be on the elliptical or doing a video while the other was running on the treadmill. We made it work. I was bound and determined once I hit the one-year cancer free mark and wasn't as healthy as I promised myself I'd be.
I'd recommend seeing if you can do it while the kids are at practice/games.
I'd also recommend something like Weight Watchers online where you can spend a few moments tracking what you're eating and making more conscious efforts to make healthier changes - if possible start by attending a one-on-one session with a Registered Dietician to see how many calories you should be consuming to meet your goals and what realistic weight loss/week really is (most people get really disheartened when they slow to 1-2 lbs/ month though it's healthy and physiologic).
Another thing is to learn to add things like fiber to your diet to help satisfy your hunger, slow how quickly you eat (takes 20 minutes to feel full), drink more water to help feel full, break your meals into 6 large snacks, etc.
Good luck!