I think you need to try and smooth things over at home first, including with your dad's girlfriend, either directly or with your dad. Spending time with your boyfriend is very different to moving in with him and his mum. How much is done for you at home and could you cope with college, job and helping around the house with your bf's mum? What if you want some privacy? What if you don't like what's on tv or the meal being cooked?
You would need to plan your finances very carefully before moving out. What if your parents stopped financial support? Could you afford to socialise, buy clothes, shoes, toiletries, mobile phone, travel and contribute to your bf, plus set aside some savings? What about medical and dental bills a bit further down the line? What if you want to learn to drive?