I don't have a solution to your question, sorry.
But I do wish you good luck.
Figure out what your priorities are. Personally, my priority is my family. But it isn't the same for everyone, and if there is no way you could be happy with your family, then take the decisions that will change that. But if there is even the smallest possibility, my suggestion is that you take it. It's kind of selfish to say "I am not happy" and move on. Try to fix things. I know you must be thinking I don't know what I am talking about, I don't know your problems, but trust me, I have had some pretty tough ones myself.
If you don't feel love for your family, and what you consider your priority is not being fulfilled, then take actions that will fulfill that priority. Just make sure you truly know what it is, and that it will not change later in life (you are taking some big steps at a very young age, and changing priorities is not a luxury you can afford if you proceed with these steps).
If you feel living "independently and responsibly" is what you want, what will satisfy emotional, physical, intellectual, and social needs, then go ahead, and you have my best wishes. Just make sure you have the right idea of what independently and responsibly really means. That is quite hard at 16, but I won't say it is impossible. Who am I to tell you whether what you are doing is wrong or right.