Networking :: Individually Address Hosts In Private Network From The Outside

The facts are as follows:

1. I have at work a regular LAN with many PCs, each with a DNS-registered public IP. Therefore I am able to address each of these PCs by their fully-qualified names and, for instance, initiate ssh sessions to any of these computers just by typing "ssh <name_of_machine>" from a terminal.

2. Within the aforementioned LAN I have just created a private network with some clients, which access the LAN through a router (a D-link DIR-825). We have created this private network for many reasons, but most importantly because we need to guarantee that the hosts in this network will remain networked among them even if the LAN goes down for any reason (which unfortunately happens often). But we still need to have access to the hosts in the private network from the LAN.

3. I am able to define port forwarding rules in the router in order to access certain services on the private network's clients. For example. I am able to access (by ssh) hosts "H1" and "H2" on the private network from a client on the LAN by defining rules for forwarding ports "P1" and "P2" on the router's public IP to TCP port 22 on the private IPs of "H1" and "H2", respectively. Then I would access each of these hosts from the LAN by using:

>ssh -p P1 [ip.address.of.router] (for accessing H1) and >ssh -p P2 [ip.address.of.router] (for accessing H2)

4. The problem with the port forwarding approach is that it is not easily scalable. For instance, If I wanted to enable ssh access to each host in the private network, I would have to define a port forwarding rule for each machine, and then REMEMBER all these port rules when initiating a ssh session from the LAN in order to point to the right host. And the problem gets worse when considering more services in addition to ssh.

5. The ideal solution would be to be have a means for addressing each host in the private network individually, in much the same way in which I address the hosts in the LAN (which have DNS-registered names). For instance, in order to access hosts H1 and H2 as in the previous example, i would like to be able to just type

>ssh [name_of_host_H1] (for accessing H1) and >ssh [name_of_host_H2] (for accessing H2)

The bottom line:

I guess I can say that what I need is some kind of combined DNS-ing and routing that allows me to communicate with the hosts in the private network from outside of it in a transparent way.

The question is: what are any possible solutions for accomplishing this? I have searched the web and found stuff about things like VPNs, reverse-proxies and NAT servers, but I really can't understand if any of these could serve to solve my problem (BTW, isn't my router doing some sort of NAT-ing already? could I just add some DNS-ing in some way?)