We have three possibilities:
1) One of the sister is the culprit.
2) Mother is the culprit.
3) Hana is just making this as an excuse to kiss her sisters (Tho this begs the question if she already knew that her sisters would compete to kiss her).
You're not thinking five-dimensionally, and as a result you missed some possibilities:
4) Hana covertly kissed one of her sisters and and is accusing her sisters to draw attention away from her own act.
5) Hana passionately kissed herself and is attempting to pin the crime on her family members.
6) An unknown sixth person kissed Hana and she merely assumed it was one of her sisters.
7) Hana was kissed by an unknown sixth person and is leveraging the opportunity to manipulate her sisters into competing to kiss her.
8) The mother is blackmailing Hana and is just making this up as an excuse for Hana to kiss her sisters.
9) Hana is blackmailing her mother to make up a story so that she would have the opportunity to kiss her sisters.
10) Hana and her mother mutually agreed to make up a story that would serve as an excuse for Hana to kiss her sisters.
11) Hana kissed the mother, and the mother, being the wise matriarch that she is, compromised with Hana and made up the story to steer Hana romantically away from her, towards her sisters.
You're forgetting the possibility of a Murder on the Orient Express situation- they're actually all culprits, and every one of them kissed her.
Seriously I swear you guys either have hyperactive over imagination or just too much free time in your hands XD