The reagent indicated in the problem introduction is not a peracid (RCOOOH). Make note of this.
The terminal O of the O-O bond is electrophilic. You're attacking the wrong oxygen.
Protonating the epoxide is unreasonable for two reasons: (1) Your epoxide has sufficient strain to undergo substitution without further weakening the R-O bond, (2) the step in which you protonated your epoxide is under polar basic conditions.
Only weakly acidic species can exist under polar basic conditions (e.g. RCOOH, H2O, H2S, etc.) . R2OH+ is too acidic for this medium.
Any aqeuous workup will be done after substitution in a separate step with a strong source of H+; or more appropriately, in situ with a source of H+.