With a model that has 2 objects one of the objects is in the wrong position once I import into Unity. In blender they look correct and the origin for both is in the same location. I’ve used other multi-object models and haven’t had this problem. Anything I’m missing?
this looks like either a pivot point OR parenting issue.
Is the skin parented to the wood pieces in blender before export?
Could also be a scale issue. Is the scale of both object correct, either 1.0 or 100? reset/zero the scale to see if that fixes the problem.
Sorry - not a blender artist, but 3D hiccups like this do not require only blender knowledge. 
Is there a reason the skin and wood pieces need to be separate objects? Guessing there are different skin types for the stretcher.