I like the images. 1 could stand to be brought up in exposure more. I disagree on cropping tighter for 1. Sometimes you need environmental shots where the subject is part of the environment. If anything maybe pulling back more.
I think in the second shot she's perhaps too close to the background and the lighting appears a little flat. Also I'm not crazy about having the subjects shoulders square to the camera. I also agree that both images look about a 1/2 stop underexposed.
Now to the first image. I like the composition and I like the pose though her facial expression isn't great. I think what would really make this image better would have been a wider aperture or perhaps a longer focal length. Blurring that background a bit more would add some needed separation and make that fence and gate a little less distracting.
I also agree on the exposure. In the first on it appears that is it pretty warm and she may have had a little sweat on her face that reflected the flash. I find using the patch tool in PS works well to remove hot spots on the face. There is one on her chin and above her right eye.