I don't think that NAT can help and I do believe that renumbering one of the LANs is necessary.
Packets that originate on the site 1 LAN destined for the site 2 LAN should go into the tunnel. But why would they do that when they are already fine where they are? The tunnel doesn't know how to "pick up" on just certain remote IP addresses. I think that's the problem.
You didn't say how the computers are getting their IP addresses or why you don't want to change all that. Well, I can imagine.
One thing you could consider is this:
Apparently there aren't so many computers that the subnet addresses are all used up. And, surely you've considered that the addresses may not repeat between sites, eh?
So, you might do this:
I will assume you have 192.168.0.0 network with 255.255.255.0 or /24 on each LAN right now.
Consider changing the netmasks to 255.255.255. or /25 along with changing the networks as follows:
Site 1: 192.168.0.0
Site 2: 192.168.0.128
Now there are 2 subnets with 126 usable addresses each, using addresses that are similar to what you have now but indeed on two different subnets and voila' the VPN will work.
At least this way the changes necessary will be minimized:
If you're using DHCP at both sites then it makes it much easier.
If the IP addresses are all static then you can choose which subnet assignment between sites entails the least work in changing IPs that are on the "wrong side" of 128.
