Normally, Modern Family splits its plots between the three families, making them all intersect at some point towards the climax of the episode. "Bad Hair Day" deviates a little from that, and spins off all 3 of its stories from one source at the start; namely, the Jay and Gloria household. It’s a nice way to structure things, and makes for a perfectly serviceable episode of television.
We’ll start with the most disconnected of the three stories. After Jay kicks Phil off his company bowling team, he’s freed up to attend Claire’s school reunion. This isn’t fantastic news for Claire, who was hoping to play a little game of "what-if" with herself with the professor she used to date. There’s some standard sitcom married-couple strife for a bit, but then the whole thing is conveniently solved by the appearance of the professor’s actual, overworked and underfunded wife.