First off, I'd have a talk with your grandmother. A 4 month old puppy is far too young to expect to be potty trained. There is no way he'll be completely trained by 6 months. I mean, maybe, but it's rare. There are Yorkies who are 3 years old and still are not completely trained. I'm not trying to discourage you, but your puppy is VERY young and will be for a while. Yorkies are a tough breed to train and that's what you signed up for when you got a Yorkie, let alone a puppy. If your grandmother is starting to get annoyed/angry with your
First -- CLEAN!
I would invest in a black light and go around and find EVERY SINGLE pee spot. Next, buy an enzyme cleaner. Regular carpet cleaners do not clean carpet effectively. Only an enzyme cleaner will completely get the smell out - even if you can't smell it, they can, and if they can smell it, they will continue to go there. I'd suggest Nature's Miracle or Simple Solution. There are other brands, and they can all be found at Petsmart. Just make sure it says it's an enzyme cleaner on the bottle.
Once you've cleaned your carpet and it is urine-free, I'd suggest buying a couple of belly bands. They are rectangles of fabric that fit around your dog's belly, covering the penis. You just put a pad or something absorbent in it and it essentially acts like a diaper. This cannot be your only solution, but will probably save a little bit of your sanity.
Make sure you change the pad after he's peed in it or every couple of hours and wipe down the belly area.
Now as far as training goes.. we trained Franklin using a potty pad... is that a possibility? That way if he has to go during the night, he can pee on a potty pad and then go outside when you're there to take him out?
Crating him after he has a mistake really is doing you no good. Once they do something, they usually forget right after so he isn't associating peeing in the house with being put in his crate. He just thinks you're mean.
When you take him outside, does he go? Keep praising him like you are.. and try to find treats that will really make his mouth water. The more positive reinforcement, the better. There are a lot of healthy human foods that will work as treats - see if he's interested in apples, or cheese, or little pieces of boiled chicken. Is he on a leash while he's out to potty? Sometimes puppies get so excited they're outside that they forget they have to potty. Keeping him on a leash (with a harness) will help keep him focused. Also, how long are you staying outside with him? Stay until he goes, unless of course it's over.. 30 minutes or so. But stay at least 15 minutes. Once you bring him inside, WATCH HIM LIKE A HAWK. The minute you see a sniff and circle, pick him up and take him outside. Confine him to one room so that you can keep a better eye on him.
It will most likely be a while before he will start giving you signs. My friend's yorkie is a year and a half and still doesn't give her signs. Your best bet is to just prevent it from happening by taking him out often. I'd say every hour until he's older. Eventually, he'll learn but don't be surprised if it takes a while to click. If you're ambitious though, you can give bell training a try. Just do a search for bell training and you'll find a lot of good advice.
Hope this helps.. feel free to PM me if you have any other questions. Good luck!