I'm unable to open any chests. Just to make sure I'm not being totally silly, I should be right clicking with the key on the lock? I've tried everything I can think of to troubleshoot including a clean install with only GottschCore and Treasure2 in case there was some sort of mod conflict. I've tried going into creative and using all key/lock pick combos I can think of on just about all lock types.

PM me and I can get let you on my server if that would help for investigating. Otherwise, here's what I'm running for local single player testing. My hosted server does have additional mods. Same issue either way.
forge-1.12.2-14.23.5.2768
GottschCore-mc1.12.2-f14.23.5.2768-v1.5.1
Treasure2-mc1.12.2-f14.23.5.2768-v1.1.0

This doesn't seem like it would have anything to do with this issue, but I did find this in my logs: [Server thread/WARN] [FML]: Potentially Dangerous alternative prefix minecraftfor namewood_mimic, expected treasure2. This could be a intended override, but in most cases indicates a broken mod.

So I messed around a little more and found that if I press LShift (sneak) while using the key/pick it gives me a result in all instances. Is that expected?

Yes, you have LShift + Use for keys, picks, locks, and the key ring.

Oh god. I see that on the readme now. Sorry!
Love the mod and appreciate your work on it.