Phil
You need to do two things.
1) You will need to NAT your source IP addresses.
So for example you have on your pix 506E
nat (inside) 1 0.0.0.0 0.0.0.0
global (outside) 1 interface
which NAT's all traffic to the outside IP address of your pix.
This may not accurately reflect your NAT setup - you may need to modify.
2) You need to present the external hosts as different host within your network.
Do you know if there is a subset of the 10.1.2.0/24 at the remote site you need to talk to ?
What you will need is a new subnet for site-A. Lets say you choose 192.168.1.0/24. This subnet must be routable to the inside interface of your pix firewall.
On your pix you need to set up static translations for these addresses to the real addresses at the other end ie.
static (outside,inside) 192.168.1.1 10.1.2.1 netmask 255.255.255.255
static (outside,inside) 192.168.1.2 10.1.2.2 netmask 255.255.255.255
etc....
Now your users when they want to connect to 10.1.2.1 at the remote site need to connect to 192.168.1.1. You can setup DNS entries to make this easier for your users.
HTH
Jon