Yeah, you might be far from home, but lots of students are too! You won't be alone if you get homesick. Plus you can always Skype, VP, send mail, etc. It's a bad neighborhood, but as long as you aren't out by yourself wandering the bad area at night, you'll be fine. Basically you just need to have some common sense and be aware of your surroundings. That's the same with ANY other big city--not just DC.
The tuition is expensive, but not more than many schools I was accepted to. It's not as expensive as an Ivy League or something. Someone already told you about VR, and that's something that'll help to pay whatever college you choose to go to. If you qualify for it, they pay for SO much. If not, then I'd just cross your fingers for scholarships. Gallaudet has many scholarships that'll pay for a good chunk of your tuition if your GPA and everything is satisfactory. Dorms aren't that bad. I wouldn't even concern myself with that at all, it's just part of the college experience.
If you do apply to Gallaudet, just letting you know that if you apply early in the fall, it's FREE TO APPLY if you're deaf. So you could always see if you get a scholarship or something before you talk to your parents about it again.
As far as talking...There's TONS of oral/mainstreamed students at Gallaudet. You won't miss talking, because when you go to the store, to the mall, or whatever, hearing people are everywhere for you to talk to. :P I'm sure hearing students wouldn't mind talking to you if you asked, but because Gally IS a deaf campus, you have to sign at all times. If you're in your dorm and your roommate talks too, then obviously that doesn't matter. Talk away.
The decision is yours in the end, but don't do anything you'll regret later on. Choose what makes YOU happy.
Just to add....."bad area" doesn't nessarily mean if you wander in, you'll get shot and killed by gangs. Matter of fact, I think unless you're buying drugs or in a gang dangerous areas can be OK.....It's not like it's Beruit or Iraq or whatever. But yeah....always be with someone in those types of neighborhoods...especially if there are high numbers of drug addicts.....
And I agree with you coolgirlspyer. TELL your parents that you want to have an AMAZING college experiance. with other deaf kids. The Deaf college experiance is NOT gonna be found at a hearing school with a handful of dhh UGs. It is SO worth it.....especially with networking for jobs later on. Yes, Gally is far away from your parents, BUT the most important gift a parent can give their kid is INDEPENDACE and not sheltering them!