I suck at explaining things but let’s give it a try.
I use the same technique as if I want to freeze the background. You duplicate the top layer in the layer palette, and tick the little box right next to the duplicated layer (it should look like an eye). That eye should appear on both the first and the last layer in the layer palette. Take the eraser and erase the part of the gif that you WANT to move, leave the rest untouched. Then you go Filter - Blur - Motion Blur. That should be it. :)