Your house being so close to the property line definitely makes things tougher.
Simply from a home maintenance standpoint, with your original plan you'd have to enter your "neighbor's" fenced area to do maintenance on that side of your house, which sucks. With your dad's plan, you don't have to go in the "neighbor's" fenced area, but now you have less than 3' to work. That would really suck for power washing, painting, replacing siding, etc. (if any of those activities are applicable).
Maintenance aside, the closer a fence can be to the real, surveyed property line, generally the less long term headaches.
In any case, I would want to stay in the good graces of the neighbor since you may need to use his property to access that side of your house at some point in the future.