I agree with most of the comments above. As much as it seems she's doing it to irritate you or being 'strong willed' she really isn't. My puppy has caught on really fast with his house-training but I've never once yelled at him or punished him in any way. It's the standard drill - newspaper in certain areas (because puppies have eight seconds worth of bladder control up until a year old - scientific fact) so he doesn't get caught short. He occasionally misses the paper but I take that as he tried to get it but I don't pay any attention to him and just clean it up. If he goes where I want him to, I say "good boy!" and make lots of fuss with him. It's all about positive reinforcement and I've learned to accept that they he have accidents - possibly all his life but that doesn't bother me. If it's an expensive carpet or something, I just don't put him in that room or on the bed until I know he's gone wee-wee
I would also not use the crate to punish her. Crates are their 'den' and that should be her comfort and time-out area and somewhere she can feel safe and secure when you're not around. The attention span in rewarding a dog is two seconds long so I should imagine that the same applies to punishment too. As irritating as it must be, I also don't think it's a good idea to yell at her or scold her as she's wee'ing in the wrong place. She DOESN'T UNDERSTAND and all she'll think is she's being punished for wee'ing at all. I bet you she's going in different places because she's confused about what you want. REMEMBER - ALL A DOG WANTS TO DO IS PLEASE YOU
. If you catch her, then put her where you want her to go and just stay on her case all the time. You'll get there!