How do I adjust the shift from #2 to #3 (middle sprocket to large one) if the shifting is very difficult and the handle requires a lot of force to turn?
I have tried to adjust the barrel in front of the cable housing underneath the grip shift.

sound like the tension on the derailer 's cable is to tight , reset the shifter to 1 , disconnect the cable from the derailer , this time when you reconnect it , keep the cable a little loser that it was before .also reset the adjustment barrel back in .

There is also a common mistake when installing cables on front derailleurs that makes the cable very hard to move. There is a little 'tab' near the pinch bolt/nut on front derailleurs, and the cable is supposed to go over, not under that tab. If the cable goes under the tab it makes the cable very difficult to pull.

New housing and die drawn cable and clean up the internals on the shift grip? first..

It was indeed the position of the cable under the tab at the front derailleur that was causing the problem.Once I moved the cable OVER the tab everything worked great, Thanks to the reply #2 for great insignt into the problem.

It was indeed the position of the cable under the tab at the front derailleur that was causing the problem.Once I moved the cable OVER the tab everything worked great, Thanks to the reply #3 for helping me with the solution.

I've done that, too. And then, several years after I learned about routing the cable correctly...................I did it again.

You're welcome.

Regards,
#3