Prey drive dog and 3 legged cat

I have a friend who adopted a tripod kitty and she has a nasty little dog that thinks all cats are vermin. She's had the cat 3 years and never has been able to get the dog to accept the cat.
I still think some dogs are just not going to accept cats, and some cats simply won't accept a dog. And if the cat is physically disabled and has a difficult time getting to safety I think it's selfish to try to keep it.
Have they tried distracting the dog with treats when he meets the cat? Get the dog to think meeting, and behaving, around the cat means a treat?
My friend is selfish....she keeps her tripod kitty locked in a room for safety purposes. 3 years that poor cat has been locked in a room - only to come out when the dog is safely away. The poor cat is so unsocialized she might as well be feral. She is terrified of everything. She thinks she is doing the cat a favor by giving it a home, and she does love this cat, but she is also being terribly unfair to it.
Maybe your friend needs to ask herself what is more important - having the kitty or making sure the kitty is safe

        I don't have a lot to offer, but maybe this will help. We adopted Jessie from the shelter when she was 8 months old. She is a GSD-Lab mix with a high prey drive too. We had two cats, and when we first brought her home she would bark at them and try to chase them around the house. She didn't try to shake them, but that may be because they were adults and too large to pick up. I asked a friend who is the manager of the local PetsMart, and  also breeds and shows dogs, for advice. She said to fill a spray bottle with water and put a small amount of vinegar in it, and to spray the solution in Jessie's direction when she barked at the cats, being careful not to get it in her face, telling her no at the same time. We also crated Jessie to give the cats and us a break. The combination worked, and after two weeks the problem was solved. As fixated as the Springer is on this kitten, I don't know if this would be enough. It will most likely take more than a few weeks. Maybe they could combine the spray with the slow introductions, and reward the dog as soon as he responds to the spray and backs off. Perhaps something safe and unappealing to the dog could be applied to the kitten's back, such as bitter apple to discourage him from grabbing the kitten.
    Springers are very high energy dogs and an activity like frisbee chasing or fly ball would really help. Also, if this dog has been spoiled and not taught basic obedience, it will be harder to get him to respond to his owner's wishes since he may not respect them as the pack leader. Let us know what they decide to do.

I have not had luck with changing a dogs behavior around cats who didn't already like cats.  It's very very frustrating and if they are really going to keep the cat then they are basically going to have to be very very diligent about keeping them seperated and, if they try to increase his exposure to the cat, then make sure he is leashed and totally in their control.  It will probably take years to get the dog able to be around the cat, if it's possible at all.  I have had bad experiences where one family member didn't realize the cat was in the room and let the dog in (not my current dogs, but fosters that I've had), and then the cat was being cornered by the dog, and once a worse situation where the dog actually got the cat in his mouth, and would have killed him, probably, but we pried his jaws open. 
Since I've been in that situation, I think it's probably too dangerous to put a handicapped kitty in that situation.  Can they rehome it?

I agree with all suggestions of rehoming, but they've fallen for the kitty and don't want to do that.  They have accepted the idea of keeping them seperated for life.    Not one I would accept personally but that's me.  I'm just trying to come up with other ideas to give them.

I'm not sure if they've tried a squirt bottle but that was something I thought I might suggest as well.  They feel the dog will only live 3 more years or so (he's 9 years old or older) so they don't think the kitty will live like that forever.  Shemp is a mostly well behaved dog, they adopted him when he was older and we've dog-sat for them before and he gets along with other dogs, even our little guy.  Maybe when kitty gets older, he might be more likely to accept her. 

But no, no formal obedience since he was pretty well behaved when they adopted him a few years ago.

Have them work on teaching a "leave it" command.  Not sure if that was already mentioned or not.

         lexible's suggestion of learning a "leave it" command is good. I just wanted to add from my previous post that wild dogs shake their prey to kill them, so it is very dangerous for the dog to get a hold of the cat again. It doesn't seem fair to the dog or the cat to keep them confined. I honestly think that the dog can be trained not to attack the kitten, but it will take a lot of work and time. IMO, if they are really interested in doing what's best for the dog and the cat, they should either rehome the cat or take the time and effort to train the dog.

     Maybe instead of them meeting through a gate, the cat could be in a pet carrier, perhaps placed on the sofa. When the dog barks , he could receive a squirt of the vinegar water mixture and either told no or leave it. As soon as he complies, he should get a special treat(piece of chicken ,hot dog), and be praised. After he learns not to bark at the cat on the sofa, the carrier could be placed on the floor and the lesson would continue the same way. Then under close supervision the cat could be let out of the crate and the dog would again be corrected and praised in the same manner. As the dog learns not to be aggressive towards the cat, they could be together for longer periods of time.

Oh, also, I've seen Angel (forpaws) suggest taking a towel and rubbing the dog down with it, then using the same towel to rub the cat down, and then vise versa.  It would transfer the scents onto one another to help them get used to each other.  I've never done it, but it sounded like something you might want to try. 

there is another scent trick that might help...but it's probably not scent as much as size that's the issue. The dog sees something smaller than him that runs away and he's gotta chase
but anyway...vanilla extract at the base of both animal's tails and the scent of the extract is so strong they'll smell alike

I have the same problem and we have about 30 cats, 4 are inside.  We adopted Trixie June 2004, she was suppose to like cats but unfortunately after a few days she thought chasing them was a better idea and did catch one or two.  What's interesting is she has gotten use to the outside cats but the ones in the house are not safe with her around.  We have a half door leading to the back of the house and that's where the cats stay unless Trix is out of the house.  We also have an x-pen that we can put up in one of the rooms.  We have tried everything to have them get a long but have finally given up she will not share the inside of the house with them. 

DH is in the process of building a 6'x6'  cat encloser that attaches to the house so the inside cats will be able to go 'outside' safely.  Possibly your friends might want to consider the same.  The inside cats are 10+ years and there is no way I would re-home them. 

As someone who has had not one but TWO of my cats killed by my dogs I can tell you this with 100% certainty - NO dog is 100% trustworthy around cats.

And a high prey drive dog is NEVER, EVER to be to trusted.  All it takes is a quick glance away and the dog has the cat by the neck, one shake and it's over.  Too fast for you to react or stop them.

I know in my heart that if my boy Riggs was ever to get hold of our cat Zoe when we weren't around, he'd kill her in an instant.  But he acknowledges us as leaders and has to be content with just staring at the cat and following her around the house when we are around.  When we are not home there is at LEAST one closed, solid-core door between them.

Lauric is right in what she said.

You can take a towel and transfer smells this way. Rub the cat then rub the dog and exchange towels on prospective critters.
 
Teaching the dog a strong "Leave It" will help, but the dog will always have to be monitored around the cat.

I have taught my dogs to leave the cats alone by also saying "Not Yours". Dilly loves cats and given a chance he will chase them. That is why it is very important to instill the Leave It command.