Are you on gamepad?

If so, my semi-educated guess: you might, in the heat of combat, be pressing on the right stick enough to trigger the "Melee" button press.

The peacekeeper correlation likely comes from it being such a tense wait-for-it-wait-for-it-FIRENOW type of weapon.

As a quick test, try this: Go into your gamepad settings, switch to "Button Puncher", instead of default. This puts Melee on the 'B' button instead of Right Stick.

Then play for a bit, and see if the problem has magically gone away. =)

(If this "solves" in, then my only recommendation from there is - if you want to keep Melee on RS - to learn to relax your grip a bit. Probably easier said than done, of course!)