The whole motto: "Modest is hottest" belies that modesty is even the point of the entire exercise. It's clearly to show your obedience to the cult, like being male and going on a mission. Being an obedient member of the cult qualifies you as a good sex partner for other obedient members of the cult, thus modesty (which doesn't mean modest, it simply means dressing in cult-approved ways) is hottest (most sexually attractive, most likely to make you a desired sexual partner among the highest status sex partners). It makes me sick that fathers, of all people, promote this stuff.
Peaking out? There'd be nothing peaking about it. It would have been a good 6 inches of garment hanging around. Of course, you know the implication of that is that not only was he wearing the short-shorts, he was also commando under them!
Reading this and I thought that the message he really sent was "Here, Daughter, let me show you the importance of modesty by being immodest myself and breaking the covenants I made in the temple to always wear my garments. Show your obedience to a set of ideals that we don't really care about ourselves."
That was a gutsy move - to make a fool of himself to show his daughter how her shorts were just not appropriate. When she would not be seen with him in public, I think he made his point! :-)