Can I link two different kinds of Macs each using different OSes?
You can't really join seamlessly two separate macs, and have it all just work out of the box, eg having one Intel based Mac that can run the Lastest OS's and One older PowerPC Mac that can run all the Classic OS's and have it all work at the same time  merged into a single OS where all apps just run together.  Something like that may be theoretically possible but it has never been done, and would require Apples full support to do so. 

So in other words Paying someone to port your old classic software to  the latest version of OS X would probably be less expensive than the solution necessary for merging two independent operating systems and architectures into one, so lets not even go there any further. 

The good news is that there are options that will allow you to independently connect two macs or emulate a classic mac enviroment within an Intel mac.

Options: 


Just use both computers (each is working fine why mess with that) and connect them to make it work for you.


Connect them physically and use each one directly. What you could do is get a KVM and an extra monitor to share between them.  A KVM would let you switch one USB keyboard, USB mouse, and monitor between the two Macs at the touch of a button or keyboard stroke. Additionally, the  second monitor could be used as constant output, for example it could be showing video content as a second display from the Intel Mac while you are working on your Classic Apps on the Power PC Mac on the KVM connected / active screen.
Another solution would be to network your two Macs onto the same network and then enable screen sharing or VNC on the Power PC mac and then connect to the Power PC from the Intel Mac, effectively giving you a picture in picture view to your older Power PC mac while working within the Intel Mac. 

Use only the newer computer and find an emulation solution to run your legacy classic application on the Intel Mac. For more information on emulating classic on Intel macs see How to run Classic (pre OS X) apps on Intel Macs 


Sheepshaver seems to be the goto solution for emulating Classic OS, so if your software can work within "MacOS 7.5.2 thru 9.0.4" than this should be able to do it for you.