My kitten wants to go outside, all the time....advice ?

Two months ago I got an adorable kitten, he was two months at the time. Now he's almost 4 months, and is up to date with his shots. I do have a collar for him with his name, and our address just in case he does run outside. So basically when I first got him, the weather was getting hot outside, so my family started barbecuing again. I'd feel bad because he'd had to be inside, while we were outside enjoying the weather. So at time my siblings, or I would carry him outside for a few minutes. At first he was subtle , but than he started running out of arms, and heading in bushes. My mom only allowed him to go to our bedrooms, living room etc, if he stays an indoor cat. That's why we stopped taking him outside, because he's literally prone to get dirty. Now he keeps meowing, and always wants to be let out. Our vet told us no, he said it was dangerous, and our kitten would fight with other cats. He acts violent if he can't go outside,or he keeps meowing. At times I let him on our drive way for a little bit, but he keeps running of to the road, or dirty places. So i don't know what to do, he's always meowing to go outside, or he acts possessed and jumps every where until we take him outside, but then he doesn't listen to us !