Hi,
When you redistribute the MP-BGP routes into RIP on PE, you have an option of specifying the metric with which RIP redistributes the routes. You can make use of this feature, set the RIP metric accordingly while you redistribute the RIP of remote CE location into local CE location. Also make the metric over the backdoor link less or more preferrable (whichever way you opt for) with offset list on that specific interface. By this way local CE receives updates with two different metric (one over MPLS provider and other over backdoor link) and the one with least metric is preferred.
Also you have to stop advertising the LAN prefixes of remote CE router to unwanted interfaces by using distribute list command. This can be done on the interface of CE connecting to PE routers where distribute list contains LAN of remote CE locations. Though split horizon stops advertising I am bit skeptical about the prefixes with different metrics works with split horizon.
If the backdoor is TDM or the ethernet link where physical layer is going down on Layer 1 issues, then better option is to have static routing with higher/lower AD than RIP over backdoor link. There is no chance of looping in this case and you have better control.
HTH
Arun
