Subnetting for an MPLS

Our company has two sites. Currently we use a router to router IPsec VPN to connect the two sites. Next month we will be upgrading to an MPLS connection. But I'm not sure how to network this configuration.

I've attached a diagram to hopefully make this discussion easier. I've also attached the visio drawing in case someone wants to modify it and re-upload it.

I want all of the devices at site 1 to have access to all the devices at site 2 and vice versa. But if there a two routers then I will need to set up a new subnet in between them to allow them to communicate.

IE:
router 1 LAN port IP = 192.6.171.254
router 1 MPLS port IP = 10.8.8.1
router 2 MPLS port IP = 10.8.8.2
router 2 LAN port IP = 192.168.111.254

I can set a default route so that any traffic comming from site 2is forwarded through the MPLS but after it get translated to the 10.8.8.0 subnet how does the router 2 know where to send the traffic?

Maybe I'm just crazy and this will work fine. Idk. I finished college so many years ago and haven't done this since. Any help you can give me will be appreciated.
MPLS-Visio.png
MPLS-Visio.vsd