the sun also rises. but where?

When I drove back to the family farm last week, I drove the southwest stretch from Madison to Dubuque in the afternoon. I commented when I got back home that it was the worst week of the year to be driving southwest at sunset, as the winter solstice is as far south as the sun gets. This led to a discussion of how far north the sunrise is during summer. Basically, the issue is this: does the sun rise and set north of due east and west. My mother insists that it does; that the sunrises at due east at the fall/spring equinox and is north of due east for sunrise from the first day of spring to the first day of fall. However, some aspects of her explanation of this to me made me wonder:

[my Mom takes a pencil and paper and is going to draw a diagram of what she is talking about. She draws two circles.]
"Okay, so the sun goes around the earth, right? The sun goes around the earth."
"Well, um, I think it's generally thought to be the other way around. The sun stands still and we, you know, go around it. And, uh, the earth also, you know, spins."
"YOU KNOW WHAT I MEAN."

Anyway, I know my mom has paid more attention to sunrises and sunsets than I ever did, so despite my intuition that the sun was always to the south for people north of the tropics (that moss grows on the north side of trees, that solar panels were always on the south roof of houses, that the gnomon on sundials always pointed south, etc.), I believed her when she said the sun rose to the northeast. And, lo, some checking on the web shows she was right.

Here's a diagram of the path of the sun on the first day of spring/winter.