Hi there, if you use the search bar at the top of the page and type in 'potty training', there will be loads of useful threads that will help you
You are TOTALLY right to disagree with your girlfriend! Spraying a 10 week old pup who cant really control their bladder/bowels is NOT a good idea! Yes she will associate pooing inside with a nasty water spray, but that wont teach her to go outside. She would most likely start pooing in places where you might not find it straight away (under the bed, behind sofa etc) or eating it, either way, not good.
Ignore the bad, reward the good!
You dont say if she is crated, but thats the best way to help with potty training imo, lots more on this when you use the search bar
If pup is in a crate, they shouldnt soil their bed, it goes against their instinct. After every sleep, play, food, etc take her out. If she doesnt poo, bring her inside and either crate her or keep her leashed to you - if shes leashed to you, you will notice straight away if she needs to poo.
Try again in 10 mins, rinse and repeat as necessary!
When she does poo outside, go crazy!! Jump up and down, be sooooo excited, tell her shes such a good girl!! Give her a tasty treat reserved for pooing outside (a tiny bit of cheese or hot dog - a high value treat!) Dogs are smart, she will associate going outside with a yummy treat, but it may take a little time.
If you keep her crated/leashed to you, there shouldnt be any accidents. However, if she does poo/pee in the house, then who's fault is it? Not the pups im afraid, it would be yours as she obv wasnt crated, leashed or you werent watching her.
Hope this helps! And welcome by the way, my Chi's name is Honey

Do you have any pics of your little bubba? x