So I'm reading the spell for the umpteenth time and I'm not sure if I'm just reading it wrong or what.
Is the Copper Core feature supposed to be able to counteract chain lightning?
It is a modified counteract check.
Normally, a successful counteract check would negate the effect being counteracted. So if you do a normal counteract check against Chain Lightning, then the entire spell doesn't have any effect on anyone.
The counteract check of Copper Core of Mantle of the Melting Heart doesn't have that normal counteract effect. It uses counteract rules to run the check with. The effect is that if it is successful, then the only target of Chain Lightning would be the caster of Mantle of the Melting Heart.
So it is a pretty good choice. Saves your allies at least. Just be sure to cast a heightened spell rank if you want to have much chance of succeeding at the counteract check.