Hello,
at first glance, it looks like both your routers are configured for RIP v1 only. Try and add 'version 2' to both routers:
OUTSIDE-R#sh run
interface Loopback1
ip address 2.2.2.2 255.255.255.255
!
interface FastEthernet0/0
ip address 10.1.2.1 255.255.255.0
duplex half
!
router rip
version 2
network 2.0.0.0
network 10.0.0.0
no auto-summary
INSIDE-R1#sh run
interface Loopback1
ip address 1.1.1.1 255.255.255.255
!
interface FastEthernet0/0
ip address 10.1.1.1 255.255.255.0
duplex half
!
router rip
version 2
network 1.0.0.0
network 10.0.0.0
no auto-summary