I added a decoupling capacity
What value capacitor?
You need a ceramic 0.1uF and I would also include a 47uF electrolitic.
Decoupling is not just about ripple it is about transients as well.
If it gets in through any of the datalines, how can I decouple them?
This is not very likely and quite difficult to eliminate. This is because any suppression of transients will also suppress the signal. Things like ferrite beads and very small value capacitors would help.
However, keep the decoupling on an have a look at how your ground is wired. Make sure it is as far away from the AC lines as possible. Also make sure it goes straight back to the arduino and it does not go on to ground any other device or component.