The issue still persists when I view my website live with the original Twenty Twelve theme. I don't know how the clear and submit buttons on the theme preview page are rendered, as they seem to work fine in contrast to the search button (i.e. not pulling up the content underneath).
I used the following code to render my button:
<input type="submit" value="Press Me" />
On that note, I did manage to fix the resizing issue for my child theme yesterday, after dabbling with the code and changing about two or three values that were related. Can't remember what they were at the moment, though.
Anyhow, my issue now is that the border on the left of the button doubles when it's pressed. Can't really figure out what's causing that either.