The bugs your mom calls stink bugs are squash bugs and the brown eggs on the under side of the leaves are their eggs. The yellow brown rot on the stem and base of the plants are squash vine borers. They are a moth but look like a black and red wasp. They fly during the day unlike other moths. I keep a fly swatter on my fence just for them. If you look on your plants stems you will see little red eggs. These are the vine borer eggs and can be picked off. It sounds like you have already been attacked however. If you cut open the base of the plants you will find a grub like creature inside that is the borer larva. After He/She is done eating it will crawl into the soil and wait until next year to leave the soil as an adult...... So you have 2 options at this point that I know of. 1) Pull Squash plants and burn or feed to chickens. 2) cut off the leaves of some of the stems that are in good shape and put them into the soil. This will allow the plant to grow roots on the good stem in order to take up nutrients and water. Since the way the bores kills the plant is by destroying the base of the plant. The problem with 2 is next year borers will be living in your garden soil.
I am trying to kill adults (when I see them), and pick off eggs. They still got me this year. Next year I am going to try screen over the plants.
So at this point I think we should just form a support group. If anyone has anything that they know works please share.