How can I alleviate my dog's shedding?

I don't especially mind it that much, i mean, sure, she leaves hair EVERYWHERE (I moved the la-z-boy to mop up a puppy puddle the other day and there was a HUGE tan hair-bunny) but owning a hair covered animal, you have to expect shedding. However, my parents HATE it (i live with them still) they are embaressed by it, they hate the hair everywhere, they hate having to lint-roll their clothes etc. they have threatened my time and again to either throw her in the backyard or take her to the shelter. She's a basenji-chihuahua mix and super sweet and adorable, it would kill me to have to do either with her. I would really REALLY prefer not to have to continuously bathe her because baths really stress her out and she screams and clings to me and snarls. I just now went outside and brushed and pulled off dead hair for 15 minutes (she's only 12 pounds, not a large dog) I got a wad the size of my fist and i brought her inside and she shook off and fur STILL flew, petted her and still flying...