What your mother says, should go.
If she has a preference against a certain breed, then you should accept this and find another breed.
Honestly, you should focus less on the price and more on the breeds. Do your research to find a breed that is well suited to both you, your mother, and your living arrangement. Remember that any "free" dog is most likely not very free at all. You still have dewormings, vaccinations(both puppy and rabies) and then spaying or neutering. Add on basic obedience or behavior modifications for a well rounded, well behaved dog.
Personally, I would avoid these pups, they just sound like they'd be a holy terror to raise. HuskyXterrier mix? Many people tend to forget that "pittbulls" are terriers, would you want an 80# jack russel? They fit into some peoples lifestyles, but most of the time, people get a "pittbull" because they look good or they are what's in style. So sadly, these giant terriers are tied out in the backyard because people get tired of their prey drive or their energy levels. I have met many well rounded, well trained "pitbulls" but most of the time, I find that they are in a living situation that makes them miserable. A miserable dog can turn into those dogs you see on the news. I know that I don't do well with terriers of any size, therefore I would never intentionally own a pittbull. Just not my kind of dog.
The Husky portion of the dog may not fit into your lifestyle as well. I have known many huskies and have found that they LOVE to wander. The breed is KNOWN for their wanderlust. They'll jump, dig, slip collars, break down fences, whatever it takes to get loose and roam. We took in a husky that was wandering the street, he was beautiful and charming, but he broke several holes in our wooden privacy fence, dug huge holes that allowed all our dogs to escape, finally one day we came home and he had taken off, never saw him again. Of course this all happened in a single week.
Do your research! Once you find a breed that is well suited to you and your family, search the pounds and local rescues. I know our local humane society, adopts any dogs out for $90, but this includes spaying or neutering and then all the vaccinations. That is actually an excellent deal and you are saving a life. If you get a breed your mother is suspicious of, she will always be suspicious of the dog and even normal puppy behaviors will be exaggerated. Get a dog everyone agrees on, everyone will be much happier.