Loner96_, as others have suggested here, your feelings of loneliness are shared by many, but I encourage you to relentlessly pursue relationships regardless of the obstacles. Heres my perspective on your situation:
Your stuttering may hurt your confidence level and will inevitably affect people's first impressions, but you can counter that with enough honesty, friendliness, and humor to overcome first impressions. After all, the eloquency of your speech does not reflect, yet alone dictate, the type of person you are. I think we all judge people initially by how they talk, then what they say, then eventually by what they do. You can help your situation by quickly jumping to that second step - by expressing an attractive personality that outweighs any of your physical flaws. In the end, whether you overcome your stuttering or not, you have control over the character you build for yourself. And a good, personable, attractive character tends to be a magnet for meeting people and making relationships in life.
Coming from a dysfunctional, unloving, disinterested family myself, I can understand having little interaction with one's closest relatives. Let me suggest though that such ties are important to pursue and maintain as best possible. I believe God created us for a purpose in life - to know and love him, and to learn how to love others. Consider, you can love your family even if they don't reciprocate. You do that by showing them respect, giving them your time, and helping out whenever the opportunity arises. In the process of engaging with them and giving unconditionally, you not only please God and set a good example for others, but you improve your own character and opportunity to grow the variety of relationships that you need and want.