Yes, the paint should be taken off completely...everywhere. You can use a DA (dual action) sander with 80 grit to remove the existing paint. Take all the paint off to bare metal, do any body work you require, epoxy prime the car. Depending on the type of epoxy primer you use, it may be block sanded and ready for paint or it may need a 2 part high build primmer applied, block sanded and paint.
Sounds easy...well it's a lot of work.
Hope this helps.