My son and family received an adorable and very smart little Maltese puppy about 8 months ago. He was about 2 months old then and they only had him about 6 months before giving him to my sons older children and ex-wife due to they just could not get him housebroken. Now after about 3 months my sons ex-wife wants to give him back due to the same problem. This little dog has lived in 3 different housholds and none of them have been home much and had the proper time to train him and I know that moving around so much is hard on him too but it seems after this long that he would have been housebroken by now. Does this breed have a history of having problems in this area and is the any advice at this point for getting him broken.

Many people do report problems with smaller dogs. I know my very capable daughter had problems with her Lhasa/Min Pin. Since then, they had good luck with a Lab and a shepherd. Could have been a problem convincing her husband to do it this way:

Housebreaking starts before you get home with the new puppy. If you don't have
A crate, buy one. I prefer the more enclosed, den like plastic ones. Skip the
Bedding. At first it gets wet, and later it can be chewed into choking
Hazards. A wire rack in the bottom will help keep the puppy up out of
Accidents at first. They are available with the crates, but a piece of closely
Spaced wire closet shelving from a home supply place is cheaper. If you
Already have a metal crate, covering it may help. Just make sure you use
Something the puppy can't pull in and chew. Dogs that start in crates as
Little puppies, accept them very well. Never leave an unattended puppy loose
In the house. If nobody can watch it, put it in the crate. I suggest letting
The dog have its crate all its life.

Choose a command and spot you want it to use. The less accessible to strays,
The less chance of serious disease. If it is a female, choosing a
Non grassy spot will avoid brown spots later. When you bring it home, take it
To the spot and give it the command in a firm, but friendly voice. Keep
Repeating the command and let the puppy sniff around. If it does anything,
Praise it. Really let it know what a good dog it is and how much you love it,
And maybe a treat. Note, being out there not only means you can praise it,
But it also keeps it from being snatched by a hawk. If it doesn't go, take it
Inside and give it a drink and any meals scheduled. A young puppy will need to
Go out immediately afterward. Go to the spot and follow the above routine.
Praising it if it goes is extremely important. If it doesn't go, take it back
Inside and put it in its crate and try again soon. Do not let it loose in the
House until it does go.

At first it is your responsibility to know and take the puppy out when it
Needs to go. It needs to go out the first thing in the morning, after eating,
Drinking, and sleeping. If it quits playing, and starts running around
Sniffing, it is looking for a place to go. Take it out quickly. You will just
Have to be what I call puppy broke until it is a little older.

By the time most dogs are about 3 months old, they have figured out that if
They go to the door and stand, you will let them out. The praise slowly shifts
To going to the door. Some people hang a bell there for the dog to paw. If
Your dog doesn't figure this out, try praising it and putting it out if it
Even gets near the door. A stern "Bad dog!" is all the punishment that is
Effective, and only when you catch it in the act and are sure you didn't miss
It going to the door. Clean up accidents promptly. I mostly keep the little
Puppies out of the carpeted rooms. Still I need the can of carpet foam
Sometimes. First blot up all the urine you can with a dry towel. Keep moving
It and stepping on it until a fresh area stays dry. A couple big putty knives
Work well on bowel movements. Just slide one under it while holding it with
The other. This gets it up with a minimum of pushing it down into the carpet.
This works with even relatively soft ones, vomit, dirt from over turned house
Plants, or anything else from solids to thick liquids. Finish up with a good
Shot of carpet foam. Note, do not let the puppy lick up the carpet foam.
Once the dog is reliably housebroken, your carpet may need a good steam cleaning.

Many people strongly strongly push cleaning up all evidence of past accidents. I am slower to suggest that. Dogs will return to the same spot if they can find it. When you see one sniffing the spot, that is your clue to run it out.