Homeschool: Spider Identity--anyone?

I opened my hot tub lid to test the chemical balance and found this spider. She was inside her spider sack and was working her way out of it. I think she had just laid her eggs and was finishing up making the sack. I called the kids out and we watched her work. She kept going all around the edges and patting it down with her legs and the short little things that look like fangs below her eyes. It was quite interesting to watch. I felt bad because I didn't want her brood hatching inside my hot tub, so when she was done I took a paint scraper and removed the egg sack from my hot tub lid. I wasn't wanting to destroy the egg sack but it was glued down so hard that I couldn't help it and tiny eggs went rolling all over the place. I had to gather them up with tape. We were surprised that they were so round and had a hard shell. I guess I always thought they would be jelly-like. We brought them in the house in our bug keeper and put some under the microscope. Wasn't much to see but was fun to try. Wish we could indentify our spider but I couldn't find any that matched it on the web (no pun intended!) .

I think you can click on the photos and see enlarged versions. If you happen to know the idenity of our spider, please leave a comment and let us know!