Cannot sync home folder with server when both are using wireless router supplied by A1.

When using the standard router supplied by A1, there is no ability to dictate the DHCP settings required to successfully bind the mobile computer to the server. This however, is a requirement in order to synchronize the home folder of the mobile computer with the home folder of the Open Directory user account. The DHCP settings required by the mediaBox used by A1 for sending IPTV content to the television prevents using the server with an arbitrary domain. Rather, A1 dictates a local domain of .home be used for all their devices.
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How to override the A1 router DHCP settings in order to allow binding and syncing of Mobile Account in OS X

In order for an Apple computer to bind and synchronize the mobile account with the Open Directory account on OS X Server the DHCP settings must receive consistent DNS information for that server. However with A1 the router allows only using the search domain of .home. However, for consistency, the search domain must match the domain name of the Open Directory server.
If your mobile account won't synchronize with the server, and the server's domain is not .home, check that the Search Domain listed in the System Preferences, Network settings is correct. It is .home if you received your DHCP lease from the wireless network router provided by A1. Change this to match the domain name for your server. If your server is named, then enter the search domain Additionally, it may be preferable to have manually entered DNS server data referencing the OS X Server itself. This ensures DNS record consistency between the client computer and the server, which is required to bind to the server and synchronize the mobile account
After changing this domain name and DNS server, it is a good idea to create a new location specifying the home network to store these DNS and search domain settings. When you are at that location use that preconfigured location, otherwise use Automatic for your Network Location.