Moving out (read description)

Ladies I need your help! My boyfriend and I have been talking about buying a house/moving out for a while now. We can afford to live on our own and pay all our own bills which is what we want. We want to be self sufficient and not leach off our parents. We are 20&22 
A little more about me: my father has Frontal Temporal Lobe Dementia which is a degenerating brain disease that is slowly killing him. He's not expected to even live much longer. It's been this way for a few years now so I have accepted it. 
With that being said I have 2 siblings a sister whose 28 and in Florida and a brother whose 26 and recently lived with us to help take care of dad but he ran off and decided to leave my mom and I high and dry. I stayed home from college to help take care of my dad even though I had an academic scholarship of 36,000$ to my dream school but I didn't go. Now I have a full time job and pay for a sitter to watch my dad so mom and I can both work. 
So my question to you ladies is should I move out? I want to so bad. I want to be independent and free of my mother (she is VERY controlling) and my brother and sister dipped out and I stayed behind and put my life on hold for 3 years to help the family and my brother couldn't even stick around so I could continue school at our local community college (so shitty..)
So why can't I just leave and let them figure it out like I had to? They got to go to college and get away. I've been trapped at home my whole life. 

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