I would attempt repairing what You already have.the Rubber Roof material will peel back quite a way and can be cut and re glued where necessary. Eternabond Tape plus a generous glob of Dicor sealant will easily cover any visible repairs.
Re framing the existing skylight is a relatively simple carpentry job .Even splicing onto existing cross members is not hard to accomplish.
The Roof sheeting will need to be cut back from the rotted area and replaced with new Plywood or OSB .
Install new Dry insulation ,a vapor barrier and use stainless fasteners and lots of Contact Cemen!