No it is NOT normal.
However, if the bitch is rejecting the pups and they are in danger, which it sounds like they are, they need to be separated from her or they may all end up injurred or dead. At this age their teeth are coming in and that makes nursing uncomfortable for the dam, but most will tolerate it. She may not tolerate it, and is overreacting and that can lead to serious problems.
While 3 weeks is early to be weaning, it can be done at this age. Start them on puppy gruel several meals a day. Let them nurse a few times a day until fully weaned, but be with her when it happens and hold her down and muzzle her if necessary and then take her back out. If she is hurting her pups she can't be left alone with them.
How is the pup that was injurred????
However, if the bitch is rejecting the pups and they are in danger, which it sounds like they are, they need to be separated from her or they may all end up injurred or dead. At this age their teeth are coming in and that makes nursing uncomfortable for the dam, but most will tolerate it. She may not tolerate it, and is overreacting and that can lead to serious problems.
While 3 weeks is early to be weaning, it can be done at this age. Start them on puppy gruel several meals a day. Let them nurse a few times a day until fully weaned, but be with her when it happens and hold her down and muzzle her if necessary and then take her back out. If she is hurting her pups she can't be left alone with them.
How is the pup that was injurred????