Yeah, i'm looking at that first video and i'm sorry but that doesn't look like glare ice. both your front and back tire had traction at one point or another.. and it looks to me that it could have been driven out of there with someone bouncing on your back bumper.

I know ice.. if that was ice and you had a tire spinning on it, there would have been zero movement.. and a spinning tire will make pseudo-ice even worse.

You gave up too easily.. you could have coaxed her out of there with 4Hi and some conjoling =)