I'd guess either your shorts are too big, or the chamois is too thick. Shorts should fit like your favorite pantyhose - like a second skin - and lots of people, me included, want a chamois only for a seamless surface, NOT for chafe-inducing padding.
Other thoughts: Are you riding in the same position for both types of riding? When it's "commuting" are you on the hoods or tops, vs. in the drops when you're "training," putting your pelvis and soft tissues in a more forward position? Are you wearing the same shoes? (If not, that could change your distance to the pedals and maybe cause your hips to rock.)
Speed comes from what you put behind you. - Judi Ketteler