To be honest, no one can 'sell' you on SBD. You have to find the diet that works best for you.
You can find out a lot about a variety of diets by reading the book written by the sisters who founded (and run) 3FC. It's really fun, a fast read, and tells you tons of pros and cons for each diet out there.
If you decide SBD is for you, you can find tons of information here, but I HIGHLY suggest reading the book. This is a diet that is very hard to follow correctly (and thus see the best results) without having read the book first.
As to your situation, I'm sorry that it's worked out like that.
Perhaps your parents could be persuaded to eat more healthy along with you? You'll be doing them a favor!
I think you can prepare your own meals easily without getting in their way by making them at times when they aren't in the kitchen and then freezing or refrigerating portions. This isn't a diet where you can eat a lot of premade food, eat out a lot, or eat food that's highly processed. You really do need to do a pretty decent amount of cooking or at least combining fresh ingredients. If you truly can't even get into the kitchen, you might find it easier to do a diet like Weight Watchers where you can eat almost anything--you lose by restricting the amount of calories you take in. They have a plan called 'Core', I believe, that has some similarities in common with SBD. You can learn a lot about WW from the chicks in the WW forum.
Yes, SBD is touted as being a diet that attacks belly fat first. I really can't tell you anything about that personally. I haven't heard anything about it on here and I carried my weight everwhere, so I don't have personal experience with it. From what I read, carrying the majority of your weight around your middle is the most dangerous body type in terms of heart disease, so it's great that you are wanting to get healthy and lose the extra weight!
Sounds like you have a sensible plan in regards to your goal.
Glad to have you with us...hope you find what you need here.