Is it possible to view two Apple IDs at the same time on the Find iPhone app?
If you add the second Apple ID as a family member on Family Sharing, you can see all your Family devices on Find my iPhone.

Or you can enter the credentials of the second Apple ID on any phone on the Find my iPhone app -or iCloud- and look for it.

If you’re willing to let some functionality out (no remotely playing sound, or locking and changing passcode), you can use Apple’s Find Friends and invite any Apple ID. You can then see the user on a map, set geofences and get informed on that user movements, but they can remove you at any time.