Wiring Combination Switch GFCI Outlet

You are correct that the red should be power to the light, except the other side of the switch should take off from the line in side of the GFCI, there is no requirement for lighting to be protected by GFCI, so do not connect to the load side. The GFCI tripped because there was a mismatch in the currents between power wire and the neutral wire attached to the GFCI.

This is based on my best guess based on the information you provided. To be certain, you should examine the wiring in the other switch box to ensure the black is unswitched power, white is neutral, and the red is connected to another wire leading to the light. The main uncertainty is how the other switch plays into this scenario, as there were not enough wires for a 3 way setup with power to an outlet as well.

Incidentally, I would suggest avoiding the push-in terminals if binding screw connections are available. Doing so is more work, but it provides a better more reliable connection, provided the binding screw is properly used.

I had a similar situation in my bathroom. I had power in the ceiling, to the light, and a 14/2 running down to the switchbox. My assumption is that the original install consisted only of the light switch, but had been "Upgraded" by everyone's favourite contractor, Some Moron. This esteemed craftsman put in a combo switch/receptacle, Jumpered the hot side of the switch to the hot side of the receptacle and then pigtailed the neutral of the receptacle to ground.

IF THIS IS YOUR SITUATION,

You need to run a new 14/3 from the ceiling to my switch location and break drywall to install a 2 gang box. The final wiring is:

Panel Black - 14/3 black. (with pigtail in switch location) Light Fixture Black to 14/3 Red. (Switched Hot - power to light) Panel White - 14/3 white.

In the 2 gang box, I took a black from the pigtail to the GFCI hot, and the white from the 14/3 to the neutral screw.

Other possibilities:

Existing 14/3 -- Do as above, but obviously you don't need to run a new cable. Check the wiring in the light box to make sure you get the switched hot right.

Double 14/2 - In this situation, you'd have 1 14/2 powering the receptacle, and another 14/2 acting as the runner for the switch. Usually black is hot, and white is switched hot. The white wire should be marked as such, perhaps with a piece of tape on the end. Wire it exactly as it is.

Power to the switch box You may have the situation where the power feed from the panel goes directly to the switch box. Usually you'll have a feed from the bottom (power) and another pair going out the top to the light. Check these with a voltage tester!

Create a pigtail on the feed black with two short pieces of black wire. One goes to the switch, the other to the receptacle. To the other side of the receptacle, attach the black to the light. This is your switched hot.

The white from the light, the white from the feed are wired together with an additional short piece of white wire which goes to the neutral of the receptacle.

Additional Warnings:
All connections go to the LINE side of the GFCI.
Do not work with power on. Turn off the breaker or fuse.
If you don't see one of the scenarios presented here, then call for professional help.