By 10 weeks of age she should be used to the leash by now.
It seems she does not like to be controlled...it's really not the leash?
What kind of leash are you using? For young pups, I usually go to the Dollar Store and buy the cheap, thin, light nylon leashes.
Let her just drag it around the house while you are watching her. I would not be carrying this pup around...give her a gentle tug on the leash...step ahead and call her with an encouraging voice.
Pack some really good treats...like tiny pieces of chicken...and wave them in front of her nose.
Be patient, and be prepared to wait her out...she will eventually come to you on her leash.
I would also get her signed up for Puppy K classes...most of them take pups after the second set of shots are completed. The instructor will give you alot of pointers.
Gina