One things that happens a lot with diets is that people look at "low fat" and think that means it's healthy. So be sure you have protein in every meal and snack for all members of the family. That fuels you for longer and you avoid the crash that comes from carbs (in sweets and white flour) that turn to sugar quickly. And of course no one can eat sweets if you don't buy them. People are only choosing what's in the house - so make some fundamental changes there. A trail mix of almonds, walnuts, or peanuts, plus a few (really, a few) dark chocolate chips and some dried fruit like raisins or craisins is a better snack than "low fat" crackers or cookies. And hydrate more - everyone should have a stainless steel water bottle (just fill with tap water - bottled water is so expensive and a real budget-buster) - a lot of "hunger" is really thirst.
Everyone should get involved in the cooking and prep - a great salad bar or taco bar can offer healthy choices. Your 15 year old likes to cook, so everyone can help be part of his prep team! Add more beans (protein and very filling) and less cheese, make healthier pizzas by adding frozen spinach (don't even defrost it) and peppers to a whole wheat crust, and go easy on the other items.
It sounds like most people are getting a fair amount of exercise except you, so try to walk on a treadmill which won't strain your back. Once you drop some weight, it will be easier to exercise. I'd say to get out of the house more - if you're all away from the kitchen except for community meal planning when you can support each other, it will help.
I think, if you aren't buying on impulse and the sweets/desserts just aren't in the house, there will be no choice but to eat healthier. Don't take all of this on yourself as the cook and planner - everyone needs to get into the act. Give each child a night to be in charge of dinner, and then you and your husband can take the other 4. Most everyone gets exercise so your problems are in the constant eating. I think, if you make some smart substitutions, you can cut back. Oven roasted potatoes (or half sweet & half regular) with olive oil and salt/pepper are a much better choice than frozen fries. Vegetable stir fry with some cubed tofu and some chicken chunks is really easy, and if you add brown rice, it makes you feel like Chinese take out. Make your own burgers with a lot of veggies added - we use low fat beef or bison or mix in half turkey, with things like spinach, beans, onions (plus their juice), horseradish, or Worcestershire sauce and a whole wheat bun. If everyone eats the meal that's on the table, and the "sweet" is fruit for dessert, you'll see that you'll all have more energy for exercise. Make sure school lunches are take-your-own leftovers or healthy wrap sandwiches instead of junk. If you want any recipes, let me know.