I am so sorry for your loss. The spots on the old quilt might be caused by dead bugs or dye migration. This article has good information on cleaning an old quilt.
http://www.quilthistory.com/cleaning.htm
As far as mishandling those old quilts - don't worry about it. Not every quilt is meant to last for generations. The ones that served a purpose as lawn blankets have probably been loved more than those that spent all their time in a cedar chest.