I'm living in a country where we need proper winter tires during that season so I have to switch between tires sets twice a year. Each switch I rotate the tires (rotation depends if the tires are direction or not) and mark the position on the one I remove for the next season to make sure to rotate them.
Tire rotation is recommended and I don't see an issue with that. The problem you facing is that your front tire "running band" (the part that touch the ground) may be worn and might need replacement and/or can affect drivability.
EDIT:
Here some rotation patterns from the MoutainViewTire.com site:
