A 10 week old puppy is a very young puppy. I think you are expecting too much of her too soon. Besides, at 10 weeks, she hasn't had all of her puppy shots, so you should be cautious about walking her too far from your house because she is susceptible to canine diseases.
She's not being stubborn. She might be frightened, or confused, or just puzzled about why she is being taken for a walk on a leash.
For purposes of house training, it is good that she is tinkling outside. Praise her for doing that. It might be better to take her back into the house after she tinkles, so that she makes some connection about going outside to do her business. In the long run, after she is grown, it will be much easier for you if she learns to "do business" as soon after being taken out as possible--it will save you, and her, from having to make long walks in downpours or other inclement weather.
Just get her gradually used to walking on a leash. And do it slowly, and make it pleasant for her. Don't expect her to walk too far, or to be particularly well behaved on a leash yet--she's really very young. If she sits down, you can sit down next to her, pet her, reassure her, then get up and see if she will walk with you. Don't force her to keep on walking at this stage of the game.
There is a lot of good info on the internet. This Web page has some good tips, and watch the video on that page about leash training.
Just remember, 10 weeks is a very young puppy. Leash training isn't the most important thing for her to master right now. She has lots to learn, and bonding with you is the main thing right now. The stronger that bond, the easier her training will be.
So, just enjoy her, and let her enjoy being with you.