I run 5 servers off one network of which 2 have WHS Remote Access Enabled. The others are accessable from the internet but no using the WHS Remote Access Setup. I know its crazy but without fully explaining each servers role I can tell you what you want to do is very possible.
If you just want your 2nd server to be used to perform client backups then all you need to do is set it up and configure it just like your first server. You can then reinstall the console software in all your clients so that they will be backed up to the new server. Each server will need to have a unique server name.
When setting the new server up it may be just easier for you to shut down the 1st server to avoid confusion between the two but WHS will let you select one from the other when setting it up and its best not to make a mistake so rather than explain the options here just shut the original server down and set the 2nd server up.
If your Router supports Reserving IP Numbers then I recommend you have it reserver IP numbers for your servers so thier internal IP Numbers will always be the same. Personally I reserve IP Numbers for all my network devices then I just put labels on them with their assigned IP Numbers and I also have them written down. At my age I need all the help I can get.
If you have used BDBB to backup you client backup data base you can then use it on the new server to restore the client backup database and keep your current data in check it thats important to you. You can also leave the client data on the original server and start fresh with the new server but you may want to lock the original backups on the old server so they will not be cleaned out. This is really upto you but I felt its worth mentioning. If your not familar with the BDBB Add-In just goto the ADD-INS TAB on this site where you can read about and download it. No server is complete with out it anyway so please check it out. Before attempting any BDBB Recovery I will tell you that you will need to download and install all the HP and Microsoft Updates so that you will have no issues with the database. Its a long story but your 2nd server will have to be at the same update level as your original.
So when you get your 2nd server configured and I am leaving out setting up Remote Access because it will require you to do some port forwarding manipulation and some of the HP Webpages may not work so at this time I do not advise you to setup Remote Access on the 2nd server. After the 2nd server is configured and ready to fly all you need to do is reinstall the client software and all your clients will then begin to be backed up by the 2nd server. Its pretty simple actually.
Now to access your files on the original server you can map the shares or you can go through the NETWORK and you will then see your 2 servers listed and you can acccess the shares by selecting the server you want. The Shared Files Folder on the desktop will be linked to the 2nd server and not the 1st but using the NETWORK its just a couple extra points and clicks. Just in case I lost you there just Click on Computer and there you will find Network.
Keep one thing in mind and this has always been the case and that is if a drive dies in your 2nd server you may lose client data because client data is not duplicated. This is the same for your current server and the reason why Alex wrote BDBB which provides a means for users to backup their client database. Its a manual process meaning you have to tell it to perform the backup but you only need to do this when there is an important change to your clients. With an available bay in the 2nd server you could easily rotate drives and perform a BDBB Backup or do like many others just connect an external drive and backup there. I stress this importance because if you read through the forums you will come accross people who have had issues and lost their client data or had an issue with their system drive and were very concerned about their client data. So using BDBB is like having an insurance policy for you client data.
Many people have multiple servers running in their home for a wide variety of reasons so what you want to do is very simple. If you want to get into remote access to the two servers well thats another story with its own level of complexity but it can be down as well.
Good Luck with your task and your 2nd server.