Also known as The Peterson Group, the Righteous Branch of the Church of Jesus Christ of Latter-day Saints or simply The Branch. In addition to the directory information listed on the LDS Movement Wiki, I have come across some additional information about this group:
In addition to their http://www.celestial-orb.com/ website, there is also a http://www.celestial-orb.org website they operate.
Although I'm not 100% positive, it appears that http://gcje.com/ may be a business website run by Christ's Church (it is confirmed that Christ's Church runs http://gcje.net. The gcje.com website is a work from home company, and there is a link to it at the bottom of the gcje.net website (look on homepage at the very bottom).
One of the emails I have for Christ's Church is firstname.lastname@example.org, while the email for the http://gcje.com/ is listed as email@example.com at the site's wiki (http://www.aboutus.org/Gcje.com). Coincidence? The phone number listed for GCJ Enterprises is 435-439-5274.
Also, the bearded man on the top of http://gcje.com/ bears a striking resemblance to the man I believe is Gerald Peterson (the group's leader) shown here - http://www.color-country.net/~shepherd/shepghost2.jpg. One of the archived pages for gcje.com that I looked at on the Wayback Machine (http://web.archive.org/web/20060203091725/http://gcje.com/), has the words "Our Founder" next to the picture, though those words are now removed.
Also the gcje.com/ website's copyright belongs to a G.C. Jones, who is referred to on http://www.color-country.net/~shepherd/ (another confirmed Christ's Church website) under the heading "Scenes of Southern Utah" (toward the middle of the page)
Hopefully all of that makes sense! The wiki entry for Christ's Church has been updated with all of this information.