In my experience, if they smell, all you have to do is give the brooder a quick clean. That gets a little bit more complicated, though, if your brooder is small. Let's say I have a bathtub of chicks: roughly 5x2. That's a whole lot of space for 6 chicks (which I had). I needed to clean that thing roughly every 3-5 days. Boy did it stink sometimes! When you have a smaller space (for instance: your current cardboard box) that might be around 1x1.5, along with roughly the same amount of chicks, the poop and uric acid covers that area VERY fast. You'd need to change it every day I'd bet. Maybe 2x every day...
Now, if your dad is having a hard time understanding that you need a bigger space for them and that you need to keep them inside, maybe let him look over a couple articles on chick raising. Helping him learn is the only way you're going to get him to understand. If he doesn't want to read, let him know that the chicks might stink just a little bit less if they get a bigger area. Where I live, you need a permit for chickens. If this happened to me, I could just report myself to the health department and my parents would get in trouble because the permit is under their names- not mine. Not saying that's the right thing to do of course, but if he's being real stubborn you could tell him that by not letting you take care of the birds properly, he is technically allowing their abuse. Just some things to do...
Anywho, I guess my main moral here is that if you can't do anything because your dad won't let you, it's time to make him let you. Stand up for yourself and your chicks! You're their "mama," and you shouldn't allow him to hurt your baby chicks!