Two things:

1- there is a checkbox for "ignore hand collisions" in your clothroom simulation setup. simply check it and the Hand lifting the skirt issue will go away.

2- go into the animation palette, select the entire arm or forearm or whatever you feel will be the easiest to modify and then delete all the associated keyframes and just put in a few appropriate keyframes to get the movement you want.  Pay close attention to your Animation Layers. 

Also, before you give yourself too much additional work, remember that only what is seen by the camera matters. Once a figure is in motion, it will not matter as much if the farside hand has some collisions if they are not apparent in the animation. 

HTH,

 
<;))%%%><<