Replace Track Lighting To Recessed Lights Utilizing 3-Way Switch
What happened is that the white from the top switch is a neutral, while the white from the bottom switch is a traveler. Hence, one of the travelers is connected directly to both the common wire and the light, and the other traveler coming from the second switch is shorted to the neutral -- which explains the weird behavior and tripped breakers.

Now that that's covered, lets fix this -- this is all at the light-junction-box:


Turn the power off at the breaker box
Disconnect everything but the bare (ground) wires and the red wires.
Connect the white from the top switch to the white from the light.
Connect the black from the bottom switch to the black from the light.
Connect the black from the top switch to the white from the bottom switch -- tag that white wire with a piece of electrical tape while you are at it.
Turn the power back on at the breaker box