The relationship would be in turmoil. Naruto has a big heart, but being hurt by Tsunade would be a major blow. He might initially be angry and confused. Tsunade, being the Hokage, has a responsibility towards Naruto as one of her villagers and as someone she has mentored to an extent. Her hurting him could shatter Naruto's perception of her as a reliable and kind leader. This could lead to a complex web of emotions, with Naruto having to decide whether to forgive and Tsunade having to prove herself worthy of that forgiveness.
If Tsunade hurts Naruto, it could cause Naruto to become more distant from her. He might avoid her, and this could have an impact on the village as well. Tsunade, on her part, would probably feel a great deal of guilt. This guilt could make her try to make amends, but Naruto may not be so quick to forgive. Their relationship would be in a state of flux, with Tsunade trying to regain Naruto's trust and Naruto trying to come to terms with what happened.
One possible plot could be that Tsunade, perhaps under some sort of mind - control or misinformation, accidentally hurts Naruto during a training exercise. For example, she might use too much force while sparring with him thinking he can handle it, but he gets seriously injured.
The story could develop with other characters getting involved. For example, Sasuke might hear about what happened and come back to the village to confront Tsunade. This would create a lot of tension and drama in the fanfiction.
One possible reason could be a misunderstanding. Maybe Tsunade received some false information about Naruto that made her think he was a threat to the village, so she took actions that ended up hurting him.
At first, their relationship would be very awkward. Naruto would be a bit shy and Tsunade might be stern. But as they get to know each other better, they could become friends. Eventually, they might develop romantic feelings. For example, Naruto could start to admire Tsunade's leadership skills and Tsunade could be impressed by Naruto's growth.
Perhaps a shared experience like fighting a common enemy could bring them closer. If they are in a battle together and Naruto saves Tsunade's life, or vice versa, it could be the start of a deeper emotional connection. Tsunade might then open up about her family to Naruto, and Naruto could share his own feelings about family, as he has always longed for one.
The relationship would become extremely complex. Naruto, who respects Tsunade deeply, would be uncomfortable with the power dynamic. He would constantly try to find a balance between respecting her as a person and fulfilling whatever the 'slave' situation entails. Tsunade, on the other hand, would be in a position of having to follow Naruto's commands, which would be a huge shift from her normal authoritative role.
Their relationship could become more of a mentor - mentee in the past. Tsunade has a lot of knowledge and experience that Naruto could learn from. Since they are in a different time, they would rely on each other more. Naruto would look up to Tsunade even more as she uses her skills to navigate the challenges of the past.
It could be a friendship - based relationship. Naruto has a way of befriending everyone, and Tsunade is no exception. The lemonaid might be a common interest that brings them closer. For example, they could start having regular lemonaid - drinking sessions where they just chat about their daily lives, Naruto's progress in his ninja skills, and Tsunade's responsibilities as the Hokage.
At first, their relationship might be rocky. Naruto is young and full of energy, while Tsunade is more mature and has seen a lot. But as time passes, they start to respect each other's strengths. Naruto respects Tsunade's leadership and medical skills, and Tsunade starts to admire Naruto's determination and growth as a ninja.
If Tsunade kisses Naruto, it could strengthen their relationship in a mentor - like way. Naruto might see it as a sign of deep respect and trust from Tsunade. He would likely feel more confident in following her guidance. For Tsunade, it could be a way of showing her pride in Naruto's growth.