I don't think that Jones reagent will oxidize double bonds. KMnO4 can dihydroxylate (sometimes even cleave to the aldehydes, but then will oxidize to the acid), but then you still have to do another step or two to open the ring and get the alcohols.
BTW, H2O2 is a poor epoxidizing agent for olefins. It does, however, work well for epoxidizing enones. For olefins, electrophilic epoxidizing agents are better (e.g. m-chloroperbenzoic acid).