The outer label is used by P devices for reachability inside the MPLS backbone, that is, how to route a packet between PEs throughout the backbone. Please note P devices usually only have knowledge of internal loop backs for reachability purpose.
The inner label is used by PEs as a way to allow forwarding of traffic within a specific VRF. Remember the route target isn't present in the forwarding plane and therefore whilst RT help routers build their tables the inner label associated with the packet tells the PE the forwarding instance the traffic belongs to.
I don't have the scenario very clear. Usually the destination for traffic originated from a CE is another CE. That makes the scenario be as follow: 1) CE-PE-P-PE-CE
or if you collapse Pe and P in one device that would even be
2) CE-PE-PE-CE
or
3) CE-PE-CE
Let's take scenario 1) as a reference:
-Source CE sends IP traffic -Source PE pushes the INNER (BGP) and the OUTER (LDP) labels. -The P device swaps the INNER label which is used to route traffic to the destination PE (1 P == PHP). -The destination PE inspect the outer label and forwards traffic to the destination CE.
Your output are a little unclear, could you please post "show ip bgp vpnv4 unicast vrf internet x.x.x.x/x" as as well as "show ip cef vrf internet x.x.x.x/32" and "show mpls ldp bindings" from both PE and P?
