I've worked with my mom on several occasions over the last 10 years to try to help her with her weight battle. The most recent attempt she was at 280. We've had many great successes and some failures over the years. Here's a few of my thoughts from working with my mom.
Mental
The greatest point of failure that I've experienced with my own mother has been emotions. We've made great progress: one time she lost 70 pounds over several months, another time, through a very strict meal regimen, she lost 30 pounds in 30 days, but the breaking point was depression and thoughts of failure. When she would hit a weight loss plateau would often be when she would give up and return to her old mode of operation.
Try to remove all emotion from this. This really requires a lot of mental reprogramming. Perhaps looking in a mirror, a certain number on a scale, seeing a certain person or a certain food triggers a depressed emotional state. Whatever those things are need to be identified and you need to retrain your brain to not go there. It's hard, but do whatever you have to do turn off those negative emotions.
Maybe it helps to think of this as your job. Maybe you think of it as a scientific endeavor. The more emotion you involve in the process, the more unstable the process becomes.
I think the starting point and by far hardest point of any weight loss plan is learning to control your emotions. You can't let depression get in your way -- easier said than done, I know -- but you have to find a way to be radically committed to change. Whatever meal plan or exercise program you undertake, you have to know this is what you are going to do every day of your life whether you see results or not. You have to do it because you have a conviction that it's the right thing to do.
Support
While there needs to be a part of you that is 100% committed to being successful even if it seems like your own family doesn't think you can actually pull this off (my mom felt that way), you need to find people you can lock arms with who will yank you back up when you are down, and you need to do the same for them. Lone rangers rarely win. Maybe it's a forum online, a local group, or check with your local hospital to see if they have a nutrition class/support group. Often times hospital-based groups have expert dieticians that can give you advice for your specific situation, keep you accountable and can be much cheaper than commercial weight loss services.
Diet
Sure, you need the mental edge to stick with a diet. That said, what I recommend to you below is one of the healthiest things you can do for yourself and causes some of the quickest results I've seen (second only to the ketogenic diet, but the diet below is actually sustainable for the long haul).
It's called the Slow Carb Diet. A guy named Tim Ferris has really promoted this, and check out that link, you will see phenomenal success stories. This is what I had my mom on when she lost 30 pounds in 30 days. During the same time, she dropped her glucose levels from a diabetic range (135) to around 85 points and dropped about 75 points from her total cholesterol.
Basically, you're eating black beans, lentils, split peas, almonds, green vegetables, and chicken.
And you avoid like the plague all dairy, all fruit, all grains and anything white (egg whites are okay though).
Spend one afternoon each week preparing all of your food. Get out the crockpot and throw in your beans and lentils. Pre-package all of your beans in ziplock bags for the week. Eat nothing that isn't pre-bagged and pre-planned. Feel free to fill up on your beans so you're not hungry. The food isn't exciting, but the results are.
If you have the fortitude to commit to that every day for the rest of your life, you will see dramatic results. You just can't help but win if you find the strength to not waiver from this diet.
Exercise
Any exercise needs to be low-impact at this point for joint health. I really recommend finding a gym that offers child care. If that isn't an option, look into getting a used elliptical machine on Craigslist and workout before the kids wake up. You should perform at least 45 minutes (and work up to more) of slow cardio every single day. Slow cardio is to keep your heart rate around 65% of your max, or generally about 110 to 120 beats per minute depending on your age. Since this type of cardio is so boring, you will want to find something engaging to watch or listen to, whether its just a good TV show or a great lecture series from iTunes U. At any rate, if you don't take your mind off the cardio, it will be much harder to perform.
Depending on how much time you have to commit, I'd also recommend working in some basic weight training to start building some muscle mass. Tons of benefits here, from endorphins to boosted metabolism.
Never look back
When a person begins to gain fat, that person's fat cells begin to grow, divide and create more fat cells. It doesn't matter what you do, those fat cells will be with you for the rest of your life. You can shrink them down to nearly nothing. But if you ever over feed them, they will come right back and return you to your heaviest weight in short order. That's why you can't ever look back.
This might sound a bit intense, but be prepared to never find joy in food again. You will find joy in your children, you'll find joy in becoming healthier every day, in doing the right thing for yourself and your family, and you'll find plenty of joy in living a significantly longer, disease-free life. But any enjoyment from food will disappear. You'll begin to eat only to live, and not the other way around.
Advanced Issues
There is a very small segment of overweight people who have a genetic disposition to being overweight. This isn't the case for most people, but certain people have a very efficient metabolism that allows them to survive on very few calories, which makes a regular diet impossible. If after a serious and strict regimen you aren't seeing any weight loss after several months, talk to your doctor to see if you may be one of these people. In such cases, bariatric (lap band) surgery may be the best way to control your weight and add years to your life.
I hope something in here will help you along in your journey. Best wishes.