We have two Labradors, a male and female from the same litter, that we got when they were two months. They are now 5 months old. They are both very friendly and loving with the kids, but the female seems to be afraid of me.
When I call for the female, who is also smaller than the male, she really avoids me. She will normally cower and urinate on the spot most times when I call her. The male dog is very confident.
My one theory is that because the male is very dominant over her and a little jealous, she is afraid he will hurt her if I show her affection.
The other possibility I have thought of is that her reaction stems from when I have been reprimanding them (often accompanied by a smack) to discourage defecating on the porch and jumping up on us and the children, but then I wonder why only she is afraid and not the male, as both have been reprimanded the same way.
UPDATE: I found an interesting article about Submissive Urination which describes a number of causes and how to address them. Thanks for all the input.