I finally had a chance to look at a tutorial that a friend sent. (She knows who she is) This is how I will remake them. It makes sense to me, which is nice. The only difference is that I will add the corner squares on opposite ends instead of adjacent ones. But she had put those into her instructions too, so that was very clear.
In case any of you ever need to make a block like this, here is the tutorial. It's a great site.
http://www.equilters.com/library/PFP...in-square.html
When I have them done, I'll let you know how it goes!