It sounds like once your other dog was gone, Shadow became very unsure of things in the home which has made her feel timid. Although it is possible that she chose your g/f as her 'person', it's also possible that losing her canine housemate has impacted her resulting in this behavior.
As many dog owners have learned, some dogs will urinate when they are excited or feeling submissive. Submissive urination occurs when a dog feels threatened. It may occur when she's being punished or verbally scolded, or when she's approached by someone she perceives to be threatening to her. It's important to remember that this response is based on the dog's perception of a threat, not the person's actual intention. Submissive urination may resolve as your dog gains confidence. You can help to build her confidence by teaching her commands and rewarding her for obeying. You should also gradually expose her to new people and new situations and try to make sure all of her new experiences are positive and happy.
Excitement urination occurs most often during greetings and playtime and is not accompanied by submissive posturing. Excitement urination usually resolves on its own as a dog matures, if it's not made worse by punishment or inadvertent reinforcement. This is clearly not the issue with Shadow since she only urinates when she's feeling a bit timid.
Luckily, there are tips and tricks to help with her new behavior towards you:
* Take your dog to your regular vet to rule out medical reasons for the behavior.
* Keep greetings low-key.
* Encourage and reward confident postures from her.
* Give her an alternative to behaving submissively. For example, if she knows a few commands, have her "sit" or "shake" as you approach, and reward her for obeying.
* Avoid approaching her with postures that she reads as dominant, for example: Avoid direct eye contact -- look at her back or tail instead. Get down on her level by bending at the knees rather than leaning over from the waist and ask others to approach her in the same way. Pet her under the chin rather than on top of the head. Approach her from the side, rather than from the front, and/or present the side of your body to her, rather than your full front.
Most importantly though, don't punish or scold her, which it sounds like you're already not doing - this would only make the problem worse.
With a lot of patience and some really yummy treats as rewards, most dogs can be trained out of this behavior.
I hope this helps!!!