Your problem isn't that you lack a method - it's that you have three different sources of distraction clashing in the same space. The room on the street is annoying, but at least you can control it; the real mess is when the people around you don't know you're studying and just keep living their normal lives.
Start with the outside noise: active noise-cancelling headphones work, but they're expensive and not everyone has them. Otherwise, try a stupidly simple compromise - put the mattress against the window, like lean it against the glass, with a rod or whatever you can find to hold it up. It absorbs a ton of traffic noise and costs nothing. Sounds ridiculous but it works; I thought of it because someone I know did it during street construction and said it made a crazy difference.
For interruptions inside the house, the real trick is making it visible that you're working. Just closing the door isn't enough - you have to communicate. Create a signal your mom actually understands: like a big post-it on the door with what time you're done, or a cord you hang up when you don't want to be bothered. I know it sounds basic, but people forget you're there if you don't remind them. Talk to your brother during a calm moment and explain when you need quiet; he's not the enemy, he just doesn't realize the computer noise reaches you. If someone knows that from 3 to 5 PM they can't make noise, they usually manage it because they know they can play freely the rest of the time. With your mom, instead, ask if you can agree that she only calls if it's urgent during those hours - give her a real time limit, not a vague one.