If you have a dynamic public IP, you can subscribe to dyndns.com and have hostname that points to your home IP external IP address.
On your router, you will need to forward the ports for RDP or any remote control application such as VNC or PC-Anywhere - you will need to check your WAN router documentation on the subject.
Once you access your home PC from the internet, you basically can telnet to the Lab if you have attached the ethernet ports of the routers onto your home switch.
If you have not, then you need to setup a terminal server and console from the terminal server to the lab routers. The terminal server will need to be connected to your home LAN for management access and you will need to forward the telnet port on your WAN router for remote access.
You can look into a terminal server, you can telnet to the terminal server and then have console access to all devices, it might take you some looking, but you can find some pretty cheap.
Cisco also has some terminal servers, but they have been discontinued and replaced with modular cards for 3800's and such. But you might be able to find some on e-bay or surfing the net. They are Cisco 2509 - 2512. You would also need an octal cable.
The third option is to configure your routers to accept telnet, then setup reverse telnet, reverse telnet would use the AUX port on your router. So you could telnet to the router, then reverse telnet to the console of one of your switches.
Here is a good quick reference from both cisco, and a quick how to from another website:
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