Hmm, kind of a tough situation. In fact, it's so complicated, I barely know where to start - but let me see if maybe I can help. I would hate to see problems develop that cost him his home or his life when there is likely a workable solution.
There are many reasons why the dog might be confused: new home, unclear age or history, so far different "training" styles with more to come (? history of hitting if hand shy), different people, different personalities, no yard, not consistently potty trained, and now not completely potty trained at his age, etc. It would be really helpful to know his background, including breeder and first home. In fact, if he came originally from a reputable breeder, that person may be a lot of help to you.
First, like in the dog thread yesterday, the first thing you need to recognize is that you have a dog that is from the Herding group and is therefore a very intelligent and active dog who is bred to work. He is not going to be happy sitting around a condo with nothing to do, and will make work for himself if you don't give him a job. And what the dogs sees as a job and what people see as a job may be two very different things (think of any bad dog behavior that comes to mind and you get the picture). So if you and your son are going to keep this dog, you'll need to commit to giving him daily exercise consistently. This could be ball playing, frisbee (not sure that's the greatest game for him, though, with his long back), agility (which may be fun for you and good exercise as well), soccer, etc. You can read about Corgis and Herding breed dogs online, there's a ton of information available. Herding dogs really need a lot of your time and supervision to make sure their energy is channeled in a good and appropriate way.
I would be very careful about how you (and others, see my post yesterday re Lab on that other thread) approach the dog if he is hand shy. If he feels threatened, in his dog mind his only defense is to growl, and then bite if the offending behavior continues. This will increase as he goes from puppyhood to young adulthood, when learned behaviors become set. Treat this dog only with kindness, but in a firm way. He should have no uncertainty that you are in charge, not him. Having your son involved complicates matters if he doesn't act the same way. (Who will be spending the most time with the dog?) My recommendation would be for you and your son to take the dog together to a group training class where you and your dog could learn a "language" to communicate effectively and you and your son would be on the same page as far as training and consistency go, because this is going to be the key to a happy life with this dog. We've had to do it in our family, too - not only between my DH and I, but with our kids, also. Consistency is extremely important, otherwise you will not get consistent behavior from the dog. Nothing is sweeter than a well behaved dog; and nothing is worse than an ill behaved one. You can have a well behaved one but it takes time and effort.
As for potty training, I can sympathize as my dog is not good about doing her business when she's on a leash, either. But I'm fortunate in that it's never been a necessity since I have a kennel for her right off the back of my house where she goes. (When we travel with her it can be a problem.) What you will need to do is to develop a routine and stick with it. Praise, praise, praise when he does go outside while on the leash - it wouldn't hurt to give him a small, very special treat when he does this. (I don't train with food except in special circumstances like this or at the end of a training session.) It would be helpful, too, if your routine included a consistent spot. I do not use puppy pads but again, my circumstances are different - I have a yard where you currently do not. If I were in your situation I might consider giving them a try, but you have to do it in a way that won't cause more confusion for the dog. The idea is to ultimately get the dog going outside, while on leash. You're probably better off just working toward that than using the pads, seeing the idea is to NOT go in the house. (Thinking out loud here, lol.) Especially where we're headed toward summer, and not in the throes of winter. Positives to taking the dog out are that it gets you out, too, and you may end up meeting some new friends you wouldn't otherwise have met had you not had the dog.

You can capitalize on the "time to go" when the dog is crated and wakes up from his nap, take him *directly* outside then and praise when he goes. Do this a hundred times without fail and he should get the idea.

You're correct in not giving him the opportunity to roam. He should be under your supervision at all times and you should catch him *before* he starts to go and run him outside. Challenging, I know. But remember, he is smart and wants do to do the right thing, and wants to earn your love and praise. So just stick with it and it should be ok.
You should pick up a copy of Good Owners, Great Dogs by Brian Kilcommons and Sara Wilson also. It is a wonderful resource for all aspects of dog ownership, written in a simple and pleasant way.
Good luck! What's his name, btw, and can we see pictures?
