DNS for WAN FAILURE

Hi,

We currently have two locations A and B, each as a 1Gbps MPLS link and there is also a 1G P2P. Each line is an independant connection and we want to provide some resiliency for the external facing services. Would we need to use an active public DNS service that provides failover public ip addresses, for example, the public IP addresses in site A can be presented on the WAN link for site B in the event WAN link A fails.

Can the service provider do anything over the P2P ( this is where I get confused as the P2P is unmanaged but could be converted I believe to a managed line simply by the addition of 1G + capable routers at each end. Can this link then act as a failover to site B for the public ip addresses for site A in the event of a failure ?