When you've researched everything the man at the lighthouse told you and found the connection to Meltzer, come back and talk to them about it.
The brothers are understandably upset and ask Rosa to leave. Do so, but have Joey stay and listen for a bit.
If you've done everything you need to do, you'll hear Paul call Charles "Scooter." That's the password you're after. (But as with Paul's password, it won't work until you've heard Paul say it in the game.)