Can you put something up to block the view? Try to make it so it doesn't stand out. Turn the cage so it does not face the sidewalk or road. You may want to cover the cage as much as you can so there is less access for people to reach into the cage. Put some locks on the doors, they don't have to be really good ones, just enough so that people can't open the door and can't get the lock off easily. Try to fasten the top of the cage to the bottom so they can't just lift it off.
Do you have a back porch you can put the cage? Depending on where you live, this could keep your rabbit from being seem other than by neighbours and even that you can block off.
As far as convincing your brother and mom, you need to talk with them. The big issue I would bring up is that it is getting colder (not sure what it is like where you are). While rabbits can do well in the cold, they don't do well moving back and forth all the time. You can't really have a rabbit outside during the day and inside at night. The coat they would grow the keep warm outside will make them too warm inside. You will need to do this in a way that will keep him inside rather than outside.
Could you find a way to make a pen to keep him in your room? If you can bunny proof your room, he should be able to be more free range and only in the cage for short periods. You could then get away with a smaller cage for just the litter box, food and water dishes and just have enough space to move around.
