"Hey dad."
"Yeah son?"
"I was thinking. Well you always took care of us, even more than usual since she left, but, I think I could be better to move to another place."
"…"
"It’s been a year, you know I can take care of myself, I’m 18 already remember?"
"Yes but that doesn’t mean you have to leave."
"But I want to, it’s very soon, I know that. But I want to, maybe I can start a new life early, and enjoy it more even if it is for a few years; not that I don't like living here but..."
"…"
"That’s not everything; the truth is that I also talked to my brother about this, he doesn’t mind if you want him to stay here, but he liked the idea. Sorry I didn’t tell you before."
"…"
"And that we both didn’t come to you, as it should be."
"…"
"Well…"
"Listen son, let’s talk about this on dinner, I need some time to think."
"Oh, ok sure."
Dinner
"Well guys, we have to talk."
"…"
"…"
"I kept thinking of your idea to leave home, and I have made a decision."
"Ok."
"What is it?"
"Um well, I don’t think you are capable to live both on your own. You have 18 and 16 respectively, one of you may be legal, but that doesn’t mean that you can leave, you may need some more time to actually be capable to take care of yourselves."
"…"
"…"
"However, if you really want to start again somewhere else, I can’t keep you here forever, you both are my sons, but I can’t control your fates. Do you at least know how to start in a new home?"
"We have some good savings, and our jobs are sent home, we can update our directions so we keep getting the work to our new house."
"Have you made a choice of your new house?"
"Ponyville looks like a nice place: quiet, friendly. Canterlot here is rather noisy, we don't usually like so much noise.
"Right, I suggested that place because a friend of mine knows it, she has parents there, I can take advantage of the village being quiet because I need concentration for my work."
"Yeah yeah I know about that."
"So…?"
"So, I think there is no point to insist, after all I have to support your decisions."
"Dad if you really don’t want us to do this it’s fine."
"No, I know that, but there isn’t anything better in a father’s life than the happiness of his sons, so, if you really want, you have my full support."
"Thanks dad, we will be fine, we promise."
"Yeah, I know son, I know you will."
Alright. Something right off the bat that's wrong.
You smash all of the quotes together; you're supposed to space them out and make it like an actual narrative, like this:
"Ponyville looks like a nice place," I noted, "It's quiet and friendly. Canterlot is normally noisy, and we've always hated noise." I had really suggested that place because a friend of mine knows it: she has parents there. I could easily take advantage of the village's quiet for concentration.
"Yeah, yeah, I know about your work." My father replied blatantly.
Unsure about his answer, I kept prodding. "So...?"
"So I think there is no point to insist, after all I have to support your decisions." He leaned back and smiled a bit. I was surprised at how well he took my decision, knowing his usually protective demeanor.
"Dad, if you really don't want us to do this it's fine..." my brother stated. I really had no idea if he actually was okay with Dad refuting our decision in the end.
"No, I know that, but there isn’t anything better in a father’s life than the happiness of his sons, so, if you really want, you have my full support." I don't recall ever being happier than I was then. For once, my Dad had supported one of our decisions that we had made on our own, and it was easily one of the biggest decisions we could ever actually make.
"Thanks Dad," I beamed, "we'll be fine, we promise."
My father got up before saying "I know son, I know you will," and walked away.
Something more like that. This seems more like a screenplay at the moment, I'll wait until you fix that before continuing with reading this story. I don't recall ever disliking a Fluttershy fic, so don't take my words harshly. You have great dialogue so far, so I'm looking forward to see how well you do narrative too.