1 Google seems perfectly happy to plot a route across the canal via the Gatun locks, the Bridge of the Americas, or the Pan American highway.  What it won't do is get you through the Darien, which is more or less accurate, getting a vehicle through there requires you to go off road, get local assistance through the  swamp, not get kidnapped by the FARC or the ELN, etc..
I'm curious what you consider the fourth crossing.  When I was there between 92-94, you pretty much only crossed at the Bridge of the Americas.  The Centennial bridge didn't exist yet, and while you could cross at the Gatun locks, the highways on the northern/Atlantic coast didn't connect to anything.  The Miraflores locks technically have a crossing, but it was pretty much only for official use, and it doesn't appear to be connected anymore.

2 Ah, is that what it is.  Thanks for the note; I didn't look closely enough.

The other crossing I had in mind was indeed the Miraflores locks.  Google Maps will generally route through any even theoretically viable connection, so I was surprised when it stopped dead.

3 Having looked closer, you're absolutely right.  Thanks!