This page talks about Minori's relationships with characters in the Senran Kagura series.
Very little is known about Minori's parents, but it is implied they had a stable relationships as Minori states the fact that her parents used to play with her all the time before they died. This could mean she was very close to them.
Minori has a very strong relationship with her adoptive caretaker -- Kurokage. After the death of her parents, Kurokage took her in and raised her alongside Yumi and the others. He used to play with her all the time in her parents place, and trained her using that same method which resulted in her treating shinobi work as a form of playing.
Minori loves Kurokage very much, and states that being with him makes it easier for her to forget the fact that her parents are no longer alive. She has also shown that his happiness means a great deal to her, and acknowledged the fact that she was being selfish when he was bedridden and continued to ask him to play with her even though she knew why couldn't.