Two big things stand out to me upon my comparison. the georgia site has far less backlinks and lower page rank than yours. You will find that the links they do have are extremely relevant in post links from other sites. On top of this they are also listed in DMoz. Their pages have great On Page SEO design and very good interlinked pages. Their site is 8 years old and likely has been well established as an authority.
Your site has a higher page rank which although that is a good thing is not an overpowering factor in ranking for a single keyword. Looking at your blog I noticed that you have made good use of interlinking with yourself for the terms you would like though the content is a little thin. What stands out most to me is that your links come from directories which have very little value compared to a relevant contextual link from the post of a site about divorces and lawyers.
I noticed you have a backlink from this page http://www.affordable-uncontested-divorce.com/ the anchor text here is "uncontested divorce blog" rather than "uncontested divorce". Really it seems like you should instead be focusing on more local terms such as "uncontested divorce new york city" for example as your site seems to be location specific. unless of course you do offer to cover cases outside new york then just going for "uncontested divorce" is fine.
Another note to add is that facebook shares don't influence the SERPs directly if at all.
The SEOMoz factors are a guideline to understanding the authority of a site and not a definite predictor of results in google since such factors are quite complicated.
to summarize:
1. age comparison.
2. relevant high value links as opposed to easy to get links.
3. appropriate anchor text for desired keyword.
bonus tips:
1. a few of your blog pages had broken image links
2. your images in your blogs have a good alt text but they link to the image source. try linking them to your about page or even the same post it is on as an image link with alt text is about the same as a text link with anchor text though you would be linking to a post you care about instead of an image location.