Stop thinking of it as a diet. Think of it as a life style change. If you are having a hard time with "cheating", then don't tell yourself there is something you CAN'T have. YOu can eat anything every once in awhile, as long as you don't go overboard
I eat pretty much anything I want too, BUT I make sure I can count the calories and I restrict the portions. And hopefully as I gain more control I can start to make healthier decisions. Heck I already am LOL. Substituting fruits for a twinkie, and water for cokes are small changes that you can make gradually.
In the end, it's all about calories burned vs. calories injested, so first just start wih getting your calorie intake under control. Then start thinking about how you can get more food for your calories (which is where fruit and veggies are a godsend!)
Good luck and you CAN do it. I thought I was hopeless because I could never find any diet or magic pill that zapped the fat away in a week. Just understand it will take time, but it will be worth it when you are a new, more healthy YOU! I had to totally change the way I though about al of this "dieting' stuff. LOL Your current weight is lower than my goal weight, so you're ahead of me!
Oh and PS..You said you were concerned about working out taking away from family time..Maybe you could get your whole family involved? Take a family walk to enjoy the outdoors, or buy some kind of workout DVD that maybe your kids may enjoy as well. There are all kinds of possibilities.