Sorry, I have to disagree about neutering.
Not only do I believe that neutering doesn't help in housebreaking, I'm convinced that it hinders it significantly, especially if done before sexual maturity.
Personal experience, while only anecdotal I admit, has demonstrated to me that a sexually whole dog is easy for me to housetrain.
(My current 8 year old whole male Yorkie, 4-1/2 pounds, has never gone in the house since he completed his housetraining at 16 weeks or so. Possibly as long as 17 weeks.)
He marks consitently outside but never inside. And his little body is just jammed packed with Testosterone! He is an example of all the male dogs I've owned. I never breed, but don't sterilize unless the welfare of the individual dog calls for it.
Think of it this way: If being unable to reproduce and to be without secondary sex characteristics and gender related hormones was beneficial to survival - wolves (and therefore dogs) wouldn't BE a sexually dichotomous species with behaviour highly influenced by their gender.
I LIKE male dogs to be MALE and female dogs to be FEMALE.
Neutering DOES effect hormone levels certainly. If you're unhappy with a dog being a MALE or a FEMALE, then perhaps you should consider a species where gender differences aren't so obviously manifested naturally. With certain pet birds it is very difficult to know which gender they are.
I'm happy to say I've prevented many people from sterilizing their pets. Sterilization can be a great thing WHEN CALLED FOR - in other words when it's in the best interest of the individual dog for a specific reason which needs to be addressed. An example is this: A 13-1/2 year old Shetland Sheepdog I once owned developed testicular cancer. His testicles were then removed and he lived until 16.
But to sterilize animals as a policy - where it isn't called for by the INDIVIDUAL need of the INDIVIDUAL dog is not, in my opinion a good thiing. Its overly intrusive at best and radically noxious at worst. Doing it with all dogs as a prophylactic measure is what I consider to be malpractice.
I believe that the desire of people to sterilize all dogs approaches zealotry and has gone to such extremes that I'm surprised that people don't claim that it's a panacea for ALL dog related problems....oh wait, some people do!
If people are so against doggy behaviour in the first place, that they hope to mitigate all of it by sterilization, why don't they get a stuffed dog instead of an actual one?
As far as housetraining:
Have patience - #1
Reward positve - #2
Ignore negative - #3
Have patience - #4
Didn't you realize when you purchased a Yorkie that tiny pipsqueaks as they are- they take longer than usual to housebreak? Well now you know! NO big deal! Just a little more work on your part. Think of it as the necessary work for saving all that money on food bills as they eat soooo little.
Yorkies are notorious for disliking cold temps. So if you're in a cold climate now, it might take weeks longer of constant attention.
Try this: Hold your dog for ALL of the time it's in the house, unless it's eating, being bathed/groomed...Have it sleep with you in your arms so you wake if it stirs.
Then when it DOES go to the bathroom outside....lots of praise and let it run around inside for 3 or 4 minutes. Then hold it all for ALL of the time until it goes out again......
Good Luck!
I find the males easier to housebreak than the females, but that could just be my perception.