A.,
You should check out the MOMS Club of South Valley. http://www.momsclubofsouthvalleyut.com/ part of www.momsclub.com We're a group of SAHM (mostly transplants to Utah, but a few born and raised here and mostly non-LDS women, but LDS women are welcome, too!) and we get together for activities for the kids AND for the moms. Kids are welcome at all activities except for the monthly Moms Night Out and Couples Night Out. There is no religious affiliation with the group, just a group of moms who need the support of other moms. Some things we do are playgroups for the kids, book club for the moms, meet for coffee, meet at parks, etc. Dues are only $25 for the year, and most of that goes towards our annual service project where we help other mothers and children in the area. Check out the website and click on the "contact us" and the Membership VP will send you more information. We'd love to have you join us for an activity so you can check out the group! It's full of wonderful women and kids and my kids and I have made so many great friends. Not being LDS myself, I completely understand how hard it is to meet new friends when the majority of your neighbors are already friends from church.
I hope you'll check us out!
K.