Potty training takes time... in phases.
Stage 1: Your daughter IS going pee, when you take her. BRAVO! This is GOOD! Praise her. She has "attained" this stage of it. MANY toddlers don't even do that. So count yourself lucky.
Stage 2: Next, when she is able to or ready, she will indicate herself and tell you she needs to go pee or poop. In time.
Stage 3: SHE will WANT to go to the bathroom at will... and know it and be able to do it.
Toileting comes in stages. Pee comprehension comes first. Then pooping is next, but harder and takes lots of time and takes longer... AND then "night time" control without accidents... is NOT attained, developmentally or biologically, until about 5-7 years old. SO keep this part in mind... or you and she will be sorely frustrated.
But this is all normal.
Don't pressure her or punish, it will only make her stressed.
I don't think it is her being stubborn or willful.... she is just not yet "able" to do it yet. This is common.
My daughter did not start to potty "train" until about 2.5 years old... she wanted to try now and then, but I did not drill her about it. I just took it casually....and over the course of a year, at her cues, I encouraged or stopped trying. Then, by 3.5 years old, she was going on her own. But when she was ready. With my son, who is 2.5 years old, he is COMPLETELY not ready... I don't even try with him yet. He is different than my daughter was. He has absolutely no interest in it, so far.
All the best,
Susan