Recently I had the same problem - two brands and one domain.
We solved it by using a splash-screen which introduced the two brands to the users who came through the home page. On the rest of the pages we added a simple text based link to the other brands website in the upper left corner. It took up minimal space and it didn't interfere with the rest of the interface. We used a hamburger menu for mobile and embedded the link inside that menu but also in the footer.
Both sites were e-commmerce sites and shared a lot of back end functionality but the controls were designed to blend in with the overall visual design of each of the brands.
Our user research showed that people had no problem navigating between the sites.
When we looked at other sites the most common solution were to use a network menu at the top of the web site which is pretty much the same as Diepers.com
Other solutions were to build a site framework that included several brand into the main navigation - for example www.gant.se (Gant Home and Gant Rugger is two sub brands to Gant) and designed the different brands sub sites according to their own identities. That way the sub brands could share the content and the functionality that isn't unique to them.