I will give your "theory" more credit than some here, but it does have some flaws pertaining to the shift in the plane of rotation. If either pole were shifted further toward the direction of the Sun than the current 22.5 degrees that exists, then one pole would be much warmer than the other, creating a greater difference in temperature at either. The hemisphere closer to the sun would likewise be warmer. This might account for one being polar, while the other was hotter than any equatorial regions now, but I don't think that the ice age theory goes along this line.

I do believe that the Earth's plane of rotation has changed, but not to the extreme that your idea suggests. If the Earth once had a plane of rotation at or near 0 degrees, and at the same time, was cover by an immensely thick canopy of clouds, than by the evenness of heating and the greenhouse effect of the clouds, the weather globally would be quite similar, without any ice caps at either pole. This would fit with the Bible's description of the Earth at the time of Genesis, and would also account for the flood of Noah and the differences between then and now.