Starting at the beginning. The original video for the Tailor Shop at Enbizaka was compromised of multiple pictures from multiple artists of piapro, and every time I watched it I finished my mind always thought "Sooo... What did the hairpin look like?" as it changed about every other image. You can only change a red kimono and green obi so much but to change the form of metal always bugged my to a certain extent.
I will now begin to look at the first "original picture. The one by Rgveta, illustrator of Chrono Story. This image was featured at the beginning with the title and end with the credits, and to confirm it's official this was the image shown in the Evils Kingdom booklet.
Similarly another official piece of artwork appeared in Evils Kingdom as well. Kayo was on the cover with all her sinner buddies. This piece was drawn by Ichika, you should know who this is. In this artwork we see the hairpin in a similar style to Rgveta's art.
Now we come to the most recent piece of official artwork by Yuu (not sure if that is the proper romanization, also not sure on gender). Yuu has done less direct work with the song series, only having illustrated Flower of the Plateau, but contributes largely to the books where there is always one of Yuu's pieces there. Most recently in the Waltz of Evil, Yuu contributed a piece of the Tailor Shop at Enbizaka. But in this piece the hairpin looks completely different! Now, it is not unheard of for something to look different when it is illustrated by a different artist. But on closer inspection it may not be so different. This pin still consists of a flower motif with a ball of the on the side of the head. It should also be noted that Kayo tailored the kimono and obi for herself, so why not alter the hairpin?
If one wants to go into theories one might say the pin seen in Yuu's artwork was the original pin and Kayo altered it into the one side barrette seen in the first arts. Who knows? Maybe she went for the side barrette instead because the original was made for a 14 year-old girl and thus to small for her head.
EDIT: I realise I missed another piece of artwork. THis piece is drawn by Suzunosuke and featured layered briefly in the Heartbeat Clocktower PV and clearly in the Evils Forest Booklet. In this picture we see the common version with a side barrete in the shape of a flower. It's not much of an addition but it's better than forgetting about it completely.