I am sorry to hear that you are struggling with this with your girl.
A couple of thoughts:
#1 - The most common problem I see that causes licking of the feet are allergy issues. This can worsen during the winter because of dry skin as well. Here is a link to an article on allergies and some early options for treatment in dogs:
#2 - If she has done this since she was a pup, it could be that it is a behavioral, safety net or blanket for her. Something thats he does for comfort. (Even if she is with all of you and happy, and maybe because she is with all of you and happy.)
#3 - Depending on where in the country you live, she could be worse during the winter months if she gets snow, ice or salt on her paws. This could trigger her to lick more.
I hope this helps!
As always, if you have further questions or concerns, please don't hesitate to ask them using the "reply" function.
I certainly don't think that vegetable oil or fish oil capsules would hurt at all.
(Not cod liver oil, that's different altogether!)
If you were going to do that, I would do so daily, and would go toward the fish oil caps. Remember, though, that when we make changes in the diet to affect the skin it takes 4-6 weeks to see results.