I am an essential oil therapist, and I have to say, Peppermint is very effective on mice - but I havn't heard it work on spiders! Besides, it is not a good idea to use peppermint oil around children under 6 and can also be bothersome to pets (as well as being a stimulant if that is a problem). I actually use lavender essential oil for all bugs. Though different oils seem to work on different bugs, lavender has to me, been a catch all. Last year I put a few drops in a small water bottle and sprayed my floor when I got ants (my son was learning to eat, throwing food everywhere and I must have missed something). They dissapeared and have not returned. (I had to be careful because the oils can take off the finish and sometimes do stain.) A diffuser would work properly for your purposes as well. A wonderful supplier is Jodi Baglien at baglien.com (she also makes an excellant all natural bug repellant)or you can find oils at any of the co-ops, Midwest Herbs and Healing in St. Anthony, or Present Moment in Minneapolis. Valerie Ann Worwood has some books that have recipes for many household uses - though there are many books out there if you look in the alternative health section.
Good luck - I would love to hear if peppermint works on spiders if you try it!