If you think she is stubborn, show her you can take it longer than her. Just ignore the behavior. Do not say a word. I would suggest you all go from one end of the house to the other to play Hide and seek with toys. Have the kids stay in one room while you hide the toys in different spots around the house.
When you all go outside and play, never offer to pick her up. There may be some fits, but once again step over her and go about your business.
Is she barefoot? It is the best way for your child to walk around at home. Make sure any shoes she wears are properly fitted. I remember a little cousin kept telling her parents she "did not like her shoes".. Once they took her for new shoes, they discovered she was 2 sizes larger! She had a growing spurt and they did not realize it..