Cisco – BGP Route installed in routing table seen as valid but not as best

By the data that you give us, this one is an interesting part. Unless you had change the neighbors for your safety, and put the conf here, i think you need to explaind why your iBGP neighbor has the same IP address of your UPDATE SOURCE? This one is like if your iBGP share your same host.

neighbor 1.1.1.1 description "R101 BGP interconnect"
neighbor 1.1.1.1 update-source 1.1.1.1
neighbor 1.1.1.1 next-hop-self
neighbor 1.1.1.1 send-community both
neighbor 1.1.1.1 soft-reconfiguration inbound

neighbor 1.1.1.2 description "R102 BGP interconnect"
neighbor 1.1.1.2 update-source 1.1.1.2
neighbor 1.1.1.2 next-hop-self
neighbor 1.1.1.2 send-community both
neighbor 1.1.1.2 soft-reconfiguration inbound

The update-source isn't used for eBGP unless you use eBGP multihop (which you aren't), and it's unnecessary for your iBGP since you are not sourcing from a different interface from the one which you are using to connect the neighbors. You should remove those lines.

You don't seem to be using communities, so you can lose the lines with send-community both. Normally you would have consistent communities on prefixes within your AS, and you would only use that when you need to send your communities to a different AS.

Your iBGP routers should be sharing their BGP routing tables already, so the soft-reconfiguration inbound shouldn't be used within your AS, but it is often used between ASes.

I'm not sure why you are prepending the same number of ASes to both the external routers. Normally you use prepending to have the external AS to prefer one of your routers over the other; you would prepend on one external link but not the other. The way you are doing doesn't seem like it accomplishes anything.

Since you want to advertise aggregate prefixes, use the aggregate-address command. This will advertise the summary routes, and based on what you commented, I think this is your goal. The aggregate addresses will be advertised as long as there is at least one route within the summary in your routing table. the summary-only means that it will not advertise the individual routes that are within the aggregate address.

I think your BGP configurations should look something like:

R101:

router bgp 1
 no synchronization
 bgp router-id 0.0.0.1
 bgp log-neighbor-changes
! network 1.0.0.0
! network 2.0.0.0
 aggregate-address 1.1.1.0 255.255.255.0 summary-only
 aggregate-address 2.2.2.0 255.255.255.0 summary-only
 neighbor 4.4.4.1 remote-as 2
 neighbor 4.4.4.1 description "R101 uplink"
 neighbor 4.4.4.1 update-source 4.4.4.2
 neighbor 4.4.4.1 route-map R1-MAP out
 neighbor 4.4.4.1 soft-reconfiguration inbound
 neighbor 1.1.1.2 remote-as 1
 neighbor 1.1.1.2 description "R101 BGP interconnect"
 neighbor 1.1.1.2 next-hop-self
 maximum-paths 2
 no auto-summary
!

R102:

router bgp 1
 no synchronization
 bgp router-id 0.0.0.2
 bgp log-neighbor-changes
! network 1.0.0.0
! network 2.0.0.0
 aggregate-address 1.1.1.0 255.255.255.0 summary-only
 aggregate-address 2.2.2.0 255.255.255.0 summary-only
 neighbor 3.3.3.1 remote-as 2
 neighbor 3.3.3.1 description "R102 uplink"
 neighbor 3.3.3.1 update-source 3.3.3.2
 neighbor 3.3.3.1 route-map R102-MAP out
 neighbor 3.3.3.1 soft-reconfiguration inbound
 neighbor 1.1.1.1 remote-as 1
 neighbor 1.1.1.1 description "R102 BGP interconnect"
 neighbor 1.1.1.1 next-hop-self
 no auto-summary
!