In my scenario I have a LAN (Named A1) with a windows 2008r2 server and some clients connected to it. I have set up a VPS and I connect to that over the internet from another LAN (Named A2). the IP ranges are the same in both LANs A1 and A2. Now Imagine we have an identical IP address in Both LANs (e.g. 192.168.1.50). Now if I open the resources of this IP, Which computer is available to me? and what if I want to connect to the other one?
If you are on the same subnet (network) as the conflicting range, the TCP/IP stack will use ARP without even attempting to route it, which means you'll see your local server only.
If you are on a different subnet, then you will connect to which ever one your Default Gateway sees first. This depends on which interface is having its Default Gateway used (the VPN interface or your LAN interface).
Your Default Gateway might have routes to both of the IP ranges, in which case it will be whichever one has a higher priority.
If your Default Gateway has both of the routes on the same priority, then you probably won't be able to access either of them (as part of your transmission might to go A1 and the other half to go A2).
If you need to access both of them, you're SOL.