Looking at the old, joint site, it appears both new dentistry practices are listed at the top of the page with patients being directed to the correct site for their doctor of choice. This to me seems an equitable solution for people landing on the old site.
For your Google search engine results, first I would clear up ownership of the Google+ account, and it appears this has already been done, though I can't tell who has what. If you don't have the Google+/Google Places ownership, then claim them, as I see the business address and phone numbers are the same. Then you'll be able to change the website to the new page for that address.
All social media links on the old page lead back to the Farhoumand Dental page rather than to the social media pages. Really, I think the Avanti owners of the old page are being fair and equitable in that page's management.
So now what you need to do is some SEO for the new site and wait. Farhoumanddental.com has a pagerank of one, and the newer two pages have no pagerank yet. When you're building a new site, it takes some time to earn pagerank, and the more time you put into updating your website, posting links on your Google+ page and social media sites, getting your address in proper directories and finding other inbound link opportunities, the sooner your pagerank will rise. Also, if the old site is no longer updated, it will sink as the new site rises. Make sure you've submitted your sitemap for the new site, but rather than worrying about the old site, focus on building the new.
One thing I would do also is go to getlisted.org and claim all the listings for the new business and if you can for the old ones as well. Then for the older ones I'd note on the listings that the business has closed and list both new ventures as on the current old site.