VPN into multiple LAN Subnets

I need to figure out a way to allow access to two LAN subnets on a SonicWall NSA 220 through the built-in SonicWall GlobalVPN server. I've Googled and tried everything I can think of, but nothing has worked. The SonicWall NSA management web interface is also very unorganized; I'm probably missing something simple/obvious.

There are two networks, called Network A and Network B for simplicity, with two different subnets. A SonicWall NSA 220 is the router/firewall/DHCP Server for Network A, which is plugged into the X2 port. Some other router is the router/firewall/DHCP server for Network B. Both of these networks need to be managed through a VPN connection.

I setup the X3 interface on the SonicWall to have a static IP in the Network B subnet and plugged it in. Network A and Network B should not be able to access each other, which appears the be the default configuration. I then configured and enabled VPN.

The SonicWall currently has the X1 interface setup with a subnet of 192.168.1.0/24 with a DHCP Server enabled, although it is not plugged in. When I VPN into the SonicWall, I get an IP address supplied by the DHCP Server on the X1 interface and I can access Network A remotely although I do not have access to Network B.

How can I allow access to both Network A and Network B to VPN clients although keep devices on Network B from accessing Network A and vice-versa.

Is there some way to create a VPN-only subnet (something like 10.100.0.0/24) on the SonicWall that can access Network A and Network B without changing the current network configuration or allowing devices on both netorks "see" each other? How would I go about setting this up?

Diagram of the network: (Hopefully this kind of helps)

       WAN1                                    WAN2
        |                                       |
[ SonicWall NSA 220 ]-(X3)-----------------[ Router 2 ]
        |                                       |  
       (X2)                               192.168.2.0/24
    10.1.1.0/24

Any help would be greatly appriciated!

The problem was not that VPN clients could not access the X3 network, any LAN device on the Sonicwall could not access the X3 network. Once a NAT entry was created to properally translate the source/destination of the packets destined for the X3 network everything worked fine. This is also described in a bit more detail in this question: Sonicwall routing between multiple subnets on multiple interfaces