This is a guess!!!

This is only a guess. Further investigation is needed to determine how the circuit is wired, and nothing further should be done until you have a complete understanding of the current wiring.

Based on your description, this is how I think it may be wired.

If this is indeed the case, then changing the wiring as follows, should get things working.

Notice I've swapped the black and white wires at Switch 2. I've also swapped the black and white wires from Cable #3, in the first switch box. Finally, I've marked the white wire from Cable #2 at both ends, to indicate that it is being used as a ungrounded (hot) conductor.

WARNING!!!

This answer is only a GUESS. You'll have to verify this wiring yourself, before making any changes. Trial-and-error wiring is not safe, and should never be done.

If you need further assistance once you have more information, please comment on this answer. I will be happy to help you.

So if this is on a traveler circuit

• Do you have two switches somewhere that controls that circuit ?

I think your logic about what you intend to do is fine. You will have a hot a neutral and a ground.

One of the things that looks off to me is that normally your switches have the traveler between them and not your luminary box. You would see here Two 4 wire romex's [red to red ]and then your 3 way power romex - perhaps you had two sconce lamp receptacles..