I have a little situation with my new German Shepherd puppy and I need some advice from people who own big breed dogs (preferably German Shepherds) and know what I'm talking about.

My German Shepherd is now 7 weeks old and no matter how hard I try and train her not to bite and use her teeth on me and my family, I don't seem to be getting through to her in any shape or form. Biting fingers, toes, feet, arms - pretty much anything that has skin on it.
She's generally quite bubbly and I love how she comes running up to you as soon as you open the door, but instead of licking your face she'll lash out at you and clamps her jaws down so hard piercing the skin of either myself or whoever is in front of her. She's clearly just enjoying the attention because she prances around the house looking for trouble like most puppies, but the biting is becoming a big issue for reasons which I'll state in a second.

I've tried everything. I use a firm "NO!" everytime she bites and I turn away and ignore her until she calms down, but it usually doesn't work and instead of her biting getting less frequent it's getting more common and harder as time goes on. Her teeth are getting sharper by the second. She has hundreds of chew toys, I've tried ice cubes, cold rope for her to chew, putting her into an empty room by herself, using a newspaper and smacking the floor to make a loud noise while using a firm "NO!" - I've tried everything I can possibly think of and nothing is working. I've tried these methods for over a week now and I'm not getting anywhere so I need some help.

I live with my family and I personally love German Shepherds, but my Mother hates them and associates them with police dogs and seems to have the impression that my dog will eventually lash out and put someone from the family into hospital. She has grown up with Labradors her whole life and doesn't seem to understand that all dogs will lash out if they are treated badly, not just German Shepherds. But, earlier today I was holding my dog while having a conversation with my Mother and because I wasn't showing any interest in her at the time she lashed out at my neck and almost took a chunk out of it. I now look like I've been bitten by a Vampire and have a rather scared Mother as a result who will now not step foot near my dog.
She literally launches herself at you with her teeth wide open ready to do some damage - It's not really coming across as play fighting anymore.

I hate shouting at dogs and will never use any physical violence towards her, but I really need to think of something to solve this problem soon before she gets out of control. I have a family of 6 and trying to control a puppy in an environment with 4 children around is not easy. If she ever lashes out at someone other than myself then I have no doubt that my Mother will end up not wanting her in the house so I need to sort this out now.

Any advice?