Need help networking a printer to a Domain Controller off its network.?

We have a Domain Controller here in our office that is used to connect users at remote locations to our billing software server. At one of our clinics the PC's are on the local Hospital's network. I need to add their printer on their network to our Domain Controller, so that when I make a VPN from each PC to our network I can add the printer to their TS Sessions.
I have tried setting the printer up using the add printer wizard and entering the printers IP address, but it cant detect a printer, I have to choose the type of network card it has, and once installed it says the printer is offline.
I cannot set up a VPN on their network at this time, and they use a SSL-VPN connection now, and the connection is terrible and the printers are somehow shared through a particular PC( I wasnt with the company) . When the SSL connection is broken, even for a short time, the printer is lost and takes about 30 min to show back up on network. Im not sure what else to do! Please give me suggestions!

The printer does have its own IP address, which is how I tried to connect to it. but the way it is set up now, it seems to be shared through a PC. Thanks for the reply.

You said that the printers are shared through a PC. That would be the reason that you are unable to address directly via an IP address. What you will probably have to do is to establish a trust relationship between your domain and the hospitals domain that will allow your domains to use shared resources. The you will need to add the printer to your domain controller by addressing it using the \\server\share method. This will require coordination between yourself and the hospitals IT staff to determine what trust and sharing requirements are needed.

The link below covers trust relationships between domains. I hope this helps.