You can not run programs installed on different Windows installations. i.e., if you have booted OS1 you can not run a program installed in a OS2. Installing a program under Windows means crating folders where the libraries are unpacked, along with the executable files, not to mention the registry modifications. All these changes happen under the OS that has the program installed, and it will not be recognized by another installation.
Example: if you have Office installed on the external HDD where you have Windows2 installed, that means Office was installed there while Windows 2 was booted. Windows 1 will not see that installation, even if it sees the files there.
You will need to install the program under the OS that is currently booted, then it will be opened by that OS.