My dog urinates, a lot.

Question
I tried doing some research when she was a puppy, and the best I could find was it was "submissive urination" and to ignore it. Well, it's been about a year and she still does it.

My lab mix seems to be very weary of people, but when she sees me or my wife she gets over happy and pees. What can be done about this?

My dog has a lot of lab characteristics and looks, even though we think she is a mix, not sure. She looks like a lab, but has a tongue like a chow. It's odd. I got another question though, how can I teach her to only play with her toys. She's already killed 2 birds and a rabbit.

Answer
There used to be a common practice among VERY BAD Labrador breeders who bred to Chow Chow or Pit Bulls to bring up bone density or coat.  This was common in puppy mill breeding and probably still is.  Your dog appears to be a Chow mix (because of the black tongue).

Submissive urination can be confused with urinary incontinence sometimes caused by spaying.  I suggest you talk to your veterinarian about this problem as it can be solved with medication.  If your dog really is demonstrating submissive urination, you will see clear body signals such as ears back, tail low and tucked under abdomen, and possibly even elevated hackles (hair on shoulders).  If you are seeing genuine submission, you need to promote your dog psychologically or stop any of your behavior which might make her feel the urge to offer submissive signals to you (such as coercive training, harsh discipline, raising your voice, or worse.)  To promote a dog, one must offer free attention and lots of praise with absolutely NO punishment or anger for any reason.  In terms of training, you need to obtain information regarding positive reinforcement training by going to karen Pryor's website and learning about how to use a clicker.  You'd be amazed the difference in behavior and companion ability your dog will achieve if you learn about to TEACH, rather than attempt to force.

Regarding the bird and rabbit situation, the Labrador Retriever was created as a HUNTING COMPANION and its instinct to retrieve "downed" animals is a huge part of its genetics; also, although the Lab was genetically designed for a "soft mouth" (so as not to damage the bird shot down by the hunter), your dog is a mixed breed.  The Chow Chow is an independent guarding breed whose hunting instinct has been taken from "eye, chase, fetch" to "eye, chase, take down", so what you're seeing is a combination of mixed signals from both breeds.  Your dog is doing what her genetics tell her and this behavior is hugely self rewarding; yelling at her or punishing her for it (which I suspect you might do if you're frustrated enough) will create the submissive posture you're seeing because she is following her instinct in order to please YOU, her PACK LEADER, and does not understand the mixed signals.  You need to accompany her outdoors if you don't want her to hunt and retrieve her "victims".  You can also, once you've understood and successfully used positive reinforcement training for simple behaviors (such as "sit"), attempt to retrain your dog's instincts by influencing her prey drive.  This is a complex behavior modification and you can feel free to re-post for methods regarding it in a few months after your positive reinforcement training has produced its first fruits.