A client of mine had an acrimonious split with their business partner. My client owns the legal business entities but unfortunately the other partner has the server/domain details. The other partner has since started a new company but has kept the old site up with the old company name and is taking business enquiries through that site but ultimately funnelling it through to their new company.My client is still trading under their original name and bought a .net domain to compete against the .co.uk. I've since created a new website for them with a CMS that they update regularly and I've got them set up using all the social media outlets (Facebook, Twitter, G+, Pinterest, YouTube) and they are also running Google AdWords for their company name. They're getting around 2k visits a month, the site is coded well, they've got good in/outbound links, meta data is all up to date, the social media is doing well and Google Analytics is showing positive results. Google Webmaster Tools seems to show everything running as best it could. The old site has been up around 3 years, it never gets updated and is coded really badly (tables and images etc) but it has obviously been indexed by Google, sits at the top spot and has it's sub-pages listed within it's result (not sure of the correct term).The new site, in comparison has been up around 4 months, sits at number 2 on Google with a few of it's internal pages at 3 and 4 and then their Facebook and Twitter accounts below that. The Google Ad for the business name sits right at the top of the page.My client is frustrated that the old site is still taking business enquirers from their legitimate customers who don't know the difference between the two domains. Every advertising drive they do for their site will still, unfortunately, also drive some business to their competitors. I've suggested to my client that it might be easier to take legal action rather then fight an SEO battle but they don't want to take this route.1) What other routes are open to overtake the old domain in search ranking?2) How much emphasis does the age of a site have in the results even if it's not updated regularly? Is it just a waiting game?3) Can two sites on Google have their internal pages listed within the one result? Or does Google only reserve that feature for one site per search term?4) Can Google take any action on a domain that is trading in this way? If we submitted a claim could they drop the old site from the results? 
Competing against the same business name in search results
seo;google;legal
I know you said the client doesn't want to get lawyers involved, but um, your client needs to get a lawyer involved. An SEO slap fight just isn't going to fix this, and if it's the route they want to go then they don't get to complain about promotions sending business to the competitor since that's kind of the core of the entire problem. Everything from here down is not any form of legal advice but rather some possible things to consider when talking to a lawyer. My client owns the legal business entities but unfortunately the other partner has the server/domain details.I read the above as that your client has the rights to CompanyName. Presumably that also means any trademarks associated with CompanyName and so on. Is the domain companyname.com? If so, your client should be trying to seize it (talk to a lawyer) because this:The other partner has since started a new company but has kept the old site up with the old company name and is taking business enquiries through that site but ultimately funnelling it through to their new company.possibly sets up a pretty good argument that the former partner is infringing on trademark and possibly even taking advantage of brand confusion if s/he is still operating in the same business space. (Talk to a lawyer.)Even if the domain isn't exactly $companyname, the fact it's established in attachment to the previous incarnation of the business might still provide some leverage. I'm actually unclear how/why your client even agreed to leave these assets with the partner. Did they somehow not consider the web site or at least domain name a business entity?Domain age is noted but not hugely important. Yes, multiple sites can show sitelinks for a given set of results, but you have little say over it happening. For example, if I search for movie reviews both Rotten Tomatoes and Roger Ebert have them, and they're not even the top two results; they sit at 1 and 3.Can Google take any action on a domain that is trading in this way? If we submitted a claim could they drop the old site from the results? Google cares about things like spam and duplicate/stolen content. This is an argument between former business owners who seem to have made some poor decisions in splitting up. I would say it's highly unlikely they're going to get involved. Alternate option: As far as the whole thing with sending some business to the other person during promotions, is it completely out of the question for your client to just re-establish under a new name? It seems to me like this split is rather botched anyway and it might be easier for everyone involved.