The way I see it, if the OP stays with his mom, he doesn't get a job (due to driving phobia), and is stuck doing various trivial things for his mother (I know that feel, bro. Why can't they do some of these things themselves? ), rather than having his own source of income and working harder towards his game design aspiration.

Living with mom = easier way. Living with dad and his chums = harder way.

I know I'm going to offend someone by saying this, but if you think too much about love and whatnot, then it becomes another roadblock into achieving what you want to do in life. The best way to decide this, and ultimately which is best for you, not others, is looking at it in a logical way.

What do you get when you live with your mom? You get a nice computer, which could help you learn more about your game design dream. But you still have no job, little money and you won't learn less about independence and overcoming obstacles, which are sorely needed to become successful in the gaming industry.
What do you get when you live with your dad? A source of income, and you don't have to drive to get one, and a father who shows interest in your goals. But you have to pay for Internet, some of the rent, and a good computer to continue with computer science and whatnot. But you also learn how to be independent and how to overcome obstacles.

The key to picking which one is seeing the bad in the good, and the good in the bad.

I'd say move to the city.