How old are you (I'm guessing 19-20)? The additional money may be a big attraction, but don't let it blind you. Although loath to say it (And I'm a teacher here!) qualifications are overatedas I don't personally feel that a lack of them represents a lack of skills. However, the world doesn't work like that and employers want qualifications, even if they are ignored as soon as you get the job. Therefore my recomendation would be to stick where you are, in a 'safe job' (your boss seems to like you, but don't push your luck), gain aditional qulaifiactions from a well respected manufacturer and re-assess your options in 2 years time, when you've finished your paint course.
The danger with going to a smaller firm, and as the 'last one in' you are going to be first out when the shit hits the fan and work becomes scarce. I worked in a garage, unqualified, but the works was piecemeal, I didn't know if I would be needed from one day to the next. Is the small firm going to put you through an aprenticeship too? Probably not and if you have to leave, you will have nothing to show for the time you've put in at the garage.
My advice would therefore be to stay where you are, seems you have it pretty nice. By showing loyalty, and a willingness to work (even if you are treated like shit, suck it up, you have a job) other options may open up. BMW is a big company and you could go anywhere within that company in the future, out of the workshop or within it. Starting up your own company may look like a good idea now, but its a lot of hassle and graft (said garage was an aircooled resto place, one man operation. The old boy is knackered at 50-odd and works 6 days a week). BMW will reward you nicely, and they seem to be doing well currently, so are likely to be around for a while. My Cousin works in quality at Aston Martin and has reached his pay ceiling because he lacks qualifications. If he'd stayed on and got some qualifications, he'd be earning substantially more. Pay isn't everything, but its worth considering how decisions now may impact later in life (as old fashioned as it sounds, live for today isn't really a responsible attitude).
A quick word on your conditions however. Your dad's advice is bad. I'm not sure how badly they treat you, but i'm sure it's no worse than I (and many others) have been treated in thankless jobs I've done (-30 in a giant freezer anyone?). As mentioned, its all part of being on the bottom rung. It will be good for you to appreciate what it's like to be at the bottom, and if you get to the top you can have sympathy to those working for you. My Dad was a quality manager for an electronics firm, answering to the board of directors yet he would periodically work the shop floor to show solidarity with the 'common' worker. Be good experience for you.
My advice: stick where you are, gain experience and then make a few more, well informed decisions when you are qualified, older and have a little more experience. You seem to have it pretty good atm