from your post I understand that you have bought an MPLS L3 VPN service with PE-CE protocol RIPv2.
the setup that you would like to implement cannot work because the router would complain of overlapping IP subnets in different LAN interfaces.
Even if this would be supported the routing would not work with same major network 172.16/16 at the two sites.
Site B can use subnets taken from 172.16.0.0/16 because RIPv2 is classless (it carries the subnet mask in routing updates).
You need to redesign and deploy an appropriate address plan, you cannot use a flat network anymore.
For example, you can use subnets /24 taken from 172.16.0.0/17 at Site A and subnets /24 from 172..16.128.0/17 at Site B.
Or to avoid to make changes at site A you can use a different major network at site B, like 172.17.0.0/16.
In short the service cannot act as a bridge, there are L2 VPN service like EoMPLS that could do that, but not the service you have bought.
routing would need configuration of router rip process on your CE routers and they need to build RIP neighborship with the local SP PE node. Propagation of routes is performed by MPLS SP in MP BGP and it is transparent to you.
my understanding is that you have bought a single L3 VPN service with an access link in site A and one link in site B.
The SP network is in the middle and does not allow to achieve your objective, because it makes a choice of single best route, and it propagates only this.
Inside Site A, PBR policy based routing based on source address can be used on CE device (the router connected to the MPLS cloud) to send traffic to RA or RB depending on the source address of traffic originated at SiteB
I make the assumption that you have a third router at site A RC that acts as CE node of site A.
I also assume a common LAN between RA,RB and RC inside siteA.
The following are on this CE node.
access-list 111 deny ip 192.168.1.0 0.0.0.255 172.16.0.0 0.0.255.255
access-list 111 deny ip 192.168.1.0 0.0.0.255 10.1.1.0 0.0.0.255.
access-list 111 permit ip 192.168.1.0 0.0.0.255 any
access-list 112 deny ip 192.168.2.0 0.0.0.255 172.16.0.0 0.0.255.255
access-list 112 deny ip 192.168.2.0 0.0.0.255 10.1.1.0 0.0.0.255.
access-list 112 permit ip 192.168.2.0 0.0.0.255 any
route-map PBR-siteB permit 10
match ip address 111
set ip next-hop
route-map PBR-siteB permit 20
match ip address 112
set ip next-hop
desc to SP MPLS network
ip policy route-map PBR-siteB
RIP configuration towards SP
the first two lines of ACL 111 are for allowing inter site routing, only traffic with a destination outside siteA have to be processed by PBR.
warning: this is just an example to show the logic of PBR .and I haven't checked all the commands
PBR works inbound on traffic received on CE router on the MPLS L3 VPN access link
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