Yes, DVDShrink is the easy and free way to do this.
I’m not sure that Adobe recommends editing mpeg files in Premiere if you still want to try it with that program. And if you just want a quick way to convert vobs to mpeg2, then I’d use a cleverly titled program called vob2mpg
Once in mpeg2 form, you’d probably have to use an mpeg editing program rather than Premiere—VideoReDo, one of the Womble products or Cuttermaran come to mind. More trouble than the Shrink method, but certainly workable.
If you aren’t too familiar with DVDShrink in reauthor mode, then look at some of the guides found at www.mrbass.org www.dvdshrink.info or www.videohelp.com There may not be an exact guide out there for removing clips though. You’ll have to use the set start and end frames tool in reauthor mode.