A Windows computer can only run applications as either a local user or as an account from the machine's domain or a trusted domain. If your local computer is not joined to the domain, it cannot launch applications as a domain user. Being joined to the domain is different than simply being connected to a VPN.
If your workstation is domain-joined, then depending on local and group policies, you can run an application as a domain user by shift-right-clicking on the program and choosing "Run as different user". If this does not work, then contact your domain administrator for help in this scenario; they may have policies preventing you from doing what you are trying to do.
Even if your workstation is not domain-joined, you can cause locally running programs to authenticate to remote computers as a different user than they are running as. If you launch a program from the console as:
runas /netonly /user:DOMAIN\Username C:\Path\To\Application.exe
The program will run as the locally logged on user, but any network access that supports Windows authentication will appear to come from the given domain account.