Hello,
If that proxy requires authentication, you should see authentication dialog when you access it in WPM recorder. There you enter domain2 account credentials and they will be saved within recording for use during playback. If you don't see authentication dialog during recording, you can try to run WPM recorder under different account that is not part of domain1 or domain2. For example create local account and use that to run WPM recorder so that authentication dialog is shown.