Any potential issues with running traces on both sides to increase conductivity?
The track does not need to be big enough to deal with the relays. The track needs to be big enough to deal with the load you place on it, and protected against higher loads than that.
This means you need to specify a maximum current that the board is expected to handle. It might be 10 A to match your relays, it might be less. Design with enough track width to match this current. If you cannot get it all onto one layer, it's OK to split it between several layers and stitch through with vias. Make sure there are enough vias so that the current is indeed shared between the tracks, without the vias becoming hot-spots.
Finally, put a fuse on the high current inlet to the board, to protect the track against accidental over current.