Overcoming fears or something more permanent?

Dusty was finally getting over his bout of fear from back in December about going outside for long periods of time, and with spring right around the corner I was looking forward to our cats being able to play outside. A stray Pitbull showed up on Thursday afternoon on our road and followed my mom's car to our house. (She was maybe a whole minute from our driveway so the dog didn't have to go far.) It tried to get in the car with my mom and kept following her and my sister into the garage as well as jumping on them. The Pit ended up chasing Dusty up a tree where he remained for 30 minutes. We finally were able to coax him down when the Pit was distracted by some workers in the nursery.
Later, we saw the dog running down the road after the workers vehicle so we waited a while, checked outside, then let Dusty out as well as took our toy dog out to potty. Bad move, because the Pit showed up again and Dusty was forced up into the tree and remained there for over an hour. (Our dog was simply picked up and brought back in, because she's awful mouthy and would want to bark at the Pit like an idiot all day.) Both Dusty and Sassy have now seen this dog and both are full of terror but also hate, mostly hate on poor Dusty's part. They don't have much experience with large dogs and what they do have is not very positive. They hated our neighbor's loud, annoying, barking Doberman to the point Dusty would fuzz up and try to protect my dad when he had to be close to the neighbor's fence.
On Friday my dad was off work and took both our toy dog and Dusty outside after a full check of our yard and looking for movement in the nursery. The Pit shows up again, and Dusty ends up in another tree for 7 hours, with it starting to rain well into the 2nd hour, before my dad could get him to a branch low enough to pluck him from the tree with a ladder. We chained the Pit up so it couldn't run around like crazy, scaring Dusty even further, and so we could take our dog out to the bathroom. We let it off and only put it on when we need to take our dog out and are in the process of trying to find a home for it. We would have given it to the animal shelter but 1.) It's a Pitbull and we know what happens to them and ours is NOT a no-kill shelter 2.) our shelter was just on the news Wednesday for its gruesome and inhumane way of treating animals. We don't think it got away from its home, it had no collar and surely someone would have been looking for it by now, its more than likely been dropped off.
Our trouble now is that Dusty is constantly in guard-cat mode and will fuzz up and start growling if he so much as hears the dog bark, and he gets a lot worse if he can see the dog through our storm door. He's not sleeping like usual, I'd be surprised if he has had 8 hours in the past 24 hours, and cats sleep about 16 hours a day or more. He seems to only rest when he's in one of our bedrooms. He refuses to stay on the floor when he's in the kitchen or living room and has to constantly be on the mantle, the tabletop, or the counter-top so he can watch the door for that dog. He's been sleeping in my room when he does sleep, after checking the other rooms in the house, and I think that's because the dog jumped on me and I cried out when he was in the tree the second time, maybe he thinks the dog hurt me or will try to hurt me, I'm not sure. It's like Dusty has a whole new set of fears and I really just want to find that dog a home and get it out of our cats lives. It's a really sweet dog but we can't have it here, terrorizing our cats with its presence and keeping our dog from using the bathroom.
Does anyone have a similar experience, and what would you suggest besides time after we've given the dog to a good home? Is there anything we can currently do? We haven't tried keeping Dusty confined to a room to see if that would keep him calm and allow him to settle down and sleep. Is there a pretty good chance Dusty will be okay after the dog is gone? Sassy hasn't been affected nearly as much but she fuzzes up and hisses when she sees it, sometimes she just hides. Dusty is pretty much a mess and I'm worried about him. We can't let him out, not that he really wants to go out, because he'll just end up in another tree. I was so upset when he was stuck up in that tree for 7 hours, my poor baby didn't deserve that. No animal deserves that.

 

Well, to be honest, you really need to remove this animal from your neighborhood. I am not a pit hater, and I agree you need to be very cautious about where you take these poor things because of gross public misinformation concerning their disposition. You may have to go out of town to find a shelter you're comfortable with. Call around to local communities and inquire specifically about their policy on pit bulls. But you honestly can't just let this animal terrorize your cats and it clearly needs a home. There are humane traps you can get from most shelters. Some will rent them and give you back the money, some will just give them to you. Unless you have already had experience with the animal, I would not directly approach it. If it does happen to be hostile, that will be very bad for you and very bad publicity for an already unfairly villainised breed.

 

She doesn't need a humane trap and the dog is not hostile.
The dog quietly let her chain it up and she said it's a sweet dog.
I know it was a long post, but if you had read it all the way to the end, you would realize that the comment "don't directly approach the dog" doesn't make sense. The dog is basically living with her while she's trying to find it a home.

But I agree with you that OP should call around to other shelters and possibly go to forums where there are pitbull lovers, or Google pit bull rescue organizations. If your local shelter is that bad, you might have to do legwork to find another shelter out of town.

Here are some sites I found:
PIt Bull Rescue Central:
http://www.pbrc.net/

Villalobos Rescue Center (they have a TV show called Pitbulls and Parolees)
http://www.vrcpitbull.net/dog/

This one is really good, Pit Bull Rescue Me. People all over the country can post pit bulls for free to find them homes.

http://pitbull.rescueme.org/