Outside collar looks to be LH thread, are you turning the right way?
Heat up the outer piece. Rigid makes a chain wrench that has a handle that is about a foot long. That will keep you from tearing up the notches in the pulley. Heat it and put the chain wrench on and she will move. Or you will find out why...
Get a spray can of Justice brothers JB-80 penetrating oil ,and spray in all the holes and threads .spray it on several times in 24 hours ,and try turning the front face of the vee
looks like right hand threads when viewed from front of pulley ,so that turning it clockwise ,would tighten the vee's