First, have you asked at your personal parish? Offer to host an afternoon park day or coffee at your home or whatever - ask to have the notice put in the bulletin for anyone interested in HSing (or actively HSing). The priest or the religious education director may be able to make introductions with families. Also consider moving up the chain with your inquiries - diocese, archdiocese, etc. You never know…
Second, have you considered any of the “generic Christian” families as a support network? The
Utah Christian Homeschool Association might be a good resource for you. They might have ideas for support beyond what they offer.
I also would suggest that you, privately (without your daughter involved), contact the various general (and likely mostly Mormon) support groups, coops, and associations and explain that you’re trying to find a peer group that is open to non-Mormons, explain your experiences and your daughter’s concerns, and ask for suggestions.
utch.org/membership/support-groups-co-ops/
uhea.org/
thehomeschoolmom.com/homeschooling-in-utah/homeschool-organizations-support-groups/
thehomeschoolmom.com/homeschooling-in-utah/homeschool-co-ops-academic-enrichment-classes/
homeschoolmagazines.com/utah-resources/utah-homeschooling-groups
If you’re anywhere near Hill AFB, you’ll find higher numbers of secular and non-Mormon religious families in the vicinity.
Also, I recall you saying you’ve moved around, in the past. How long do you anticipate being in Utah?
Finally, if you do homeschool, you might consider offering to run a program for the Catholic kids in the area so that your daughter could stay in touch with her friends. (I don’t know what Catholic clubs there are. I’m thinking along the lines of scouts, 4-H, etc, but from a religious perspective. There must be something you could start.)
I’m not sure I understand why she wouldn’t continue to see her current friends, if she started home educating. She wouldn’t see them every day, necessarily, but she certainly could continue to have them over to hang out, etc. Honestly, I’m a little concerned by your comment that if she left school, she’d only have access to “mom and dad”. Why is that the case?