The problem is with the weight painting. As to why it weighted to the left hand, I don’t know. In weight paint mode you can select the right hand deformation bone and click weights->Assign Automatic Weights from Bone. Make sure options->Auto Normalize is checked before doing this. This way it will only Auto weight that one bone and not mess up the other weighting you’ve done. Auto Normalize should remove the weighting of the right hands vertices from the left hand vertex group.
**Edit** is there a vertex group for the right hand’s deformation bone?
