You know, if she is that tiny, I would find a rescue group. Tiny dogs are always easy to place, and in fact it is very hard to find a small dog available for rescue. Her housebreaking issues are only going to get worse if you have to keep leaving her alone for 12 hours. I would find a local rescue group, preferably a breed-specific one, and tell them about your change in circumstances, and I bet they will find her a home very quickly.

That is actually better than trying to do it yourself, because a rescue group will be equipped to foster and screen.

And seriously, you should do it right now. Because this is no way to live, not for her and not for you.

Good luck.