As a couple of hints:
There is no true ground but ground - that is, an electrical wire to a metal rod driven into the planet itself. The word "ground" as it's used today in electronics just means "the point I will decide is the source of 0.000000V and a reference against which all other voltages are measured."
In this setup, you do not have multiple grounds. You have - and want, as a matter of fact - only a number of isolated, not-connected voltage sources. You want this to act like individual batteries, right down to not having a ground. Batteries don't have a ground terminal, they only have plus and minus terminals.
I would recommend going back into Eagle and re-naming those things Vminus1, Vminus2, etc.
As to the mains wiring: first, this is NOT a complete nor necessarily accurate description of how to do this safely. You must take responsibility for your own wiring safety. If you do not already know how to wire AC power line wiring safely, I advise you NOT to proceed until you get training or assistance to do it safely.
The ground terminal coming in from the AC power line is a real ground. It's tied through a series of metallic conductors to a rod driven into the dirt of the planet, or is if the wiring you plug into is wired correctly, but that's another story. It's called "safety ground" because it can protect you against electrocution in certain specific conditions. Those conditions are (1) you use a completely enclosing metal box around your circuits (2) that safety ground wire is solidly wired to the metallic enclosure so that any fault currents from the two other AC power wires are shorted to the enclosure. This will blow the AC line fuse. Oh, yeah: (3) there must be an AC line fuse. And (4) the AC power wiring must be wired to meet safety codes.
As an aside, you're missing a diode with anode to output and cathode to input across the voltage regulators. This protects the regulator chip if the input DC to it is shorted. Otherwise, it can die if the filter cap (for instance) shorts.
See the "Spyder" articles and "Power Supplies Basics" at http://www.geofex.com