Your network topology is still not clear, but I can provide some answers anyway...
The WRT54G is a multi-function router (includes NAT, WAP, DHCP server, stealth firewall, VPN server), not just a WAP (wireless access point) which is just a hub.
[b][i]"We have a 10.x.x.x network and the Linksys are on the 192.168.1.x network."[/i][/b]
What do you mean by this? Does this mean the "public" side of the WRT54G is a 10.X.X.X address and the "private" wired/wireless side is 192.168.X.X? The Linksys WRT54G is always on two networks, a public wired one and a private wired/wireless one.
[b][i]"We are able to RDP to a computer at each of the sites, I was wondering if the computer at each of the sites could be configured to be on both networks at once, to access the router"[/i][/b]
If that computer that you can RDP to can see the Linksys, maybe. If it has one NIC that is on the "private" side of the Linksys WRT54G, yes. If it has one NIC that is on the "public" side of the Linksys WRT54G, yes if the "Remote Management" feature of the WRT54G is turned on.
[b]Management of the Linksys WRT54G[/b]
Your Linksys WRT54G can be managed from either the "public" or "private" side of the NAT. From the "private" side of the NAT, just point a browser to 192.168.1.1 (or whatever you changed it to). This is always available. From the "public" side (which is stll private for you, your private 10.X.X.X network I presume), you can also manage it just by pointing a browser to the 10.X.X.X IP address that is assigned to that particular Linksys WRT54G. But... This "public" management interface is off by default. In the Linksys WRT54G, it is called "Remote Management" (Administration -> Management -> Remote Management).
[b]Questions:[/b]
Answers to these questions will clarify how your network is set up.
Q6. When you RDP to a computer at each site, what IP do you use to access it? Is it a 10.X.X.X IP?
Q7. Is the computer you RDP to hardwired to the network? Does it have one NIC? More than one? That is, which network(s) is it directly connected to?
Q8. How is the RDP computer connected to the Linksys WRT54G network-wise?
Q9. Is the WRT54G used just to provide wireless network access? Or, is the "private" 192.168.X.X network also used for hardwired PCs as well?
Q10. Are there any other routers at each of the 80 sites? Or, just the WRT54G?