Wa alaykum salam bro,
Your circumstance is not entirely within your control. It is not your fault that the family is dysfunctional.
some people say that it could be because of the sins of my parents
I would ignore these people. In my opinion, they're just gossip mongers who don't know when to keep their tasteless thoughts to themselves.
Verily in the remembrance of Allah do hearts find rest. You know this already Ma sha Allah. Continue being the best Muslim you can be and recite as much Quraan as you can and do as much dhikr and remembrance of Allah as possible. Apply yourself in your worldly education and work also to the best of your ability and make constant dua to Allah for help, forgiveness, jannah and all other permissible good things. When you feel down and don't know what to do, surrender all your problems onto Allah and have full trust that he will help and resolve every minute issue of yours until you feel content.
Be strong and ignore any silly things people say.