Talking about relationships means relationship between Protagonist and other characters. Also Auxiliary Characters have relationship with each other too.
Usually we divide characters into three groups :
Helpers are the one who help protagonist. they could be partners,coach,sidekicks,friend and anyone else who is with protagonist.
Hinderers are the one who against protagonist, they prevent protagonist to reach it's goal.
Some characters have different role, for instance they start off as a friend, and jealousness make them be hamper, and later return to be on the side of protagonist.
Mixing them up : to keep the story moving you need to move helpers and hampers around
And the rest
The rest of characters are the one who protagonist know them, it start from lovers to the one he knows less. these characters are required in the story, they can be helper or hamper, the can divulge character or act to affect the protagonist. To paint your story you can use these characters as a palette of colors.
Auxiliary characters are important and useful, but sometimes it doesn’t. these people could be the one in service industries, guests at parties, parents, customers and anyone that come in a scene for a reason.
Relationship between family member are very interesting. you can choose the one you love, your friends and the ones you know. family members are the one you should love them, if you don’t want it too. families and other relationships are different, families are comfortable, you can raise emotion with family members quick and easy. they understand each other quickly in a way that other characters can’t.they can talk by code, in a way that outsiders don’t understand it. they can love and hate each other, they often fight with each other, but they are allied against outsider.
Lovers are also a form of family. they can make a part of history that family relationship can’t do it, bind lovers are so close and can shattered in a way that is not possible for family bonds. Lovers chose each other and they can break to love or continue it at any time.
Enemies are in all shapes and sizes, enemy cannot be separate from others. relationship between antagonist to the protagonist is enemy’s importance in the story.
The first thing you need to do is to establish important things for your main character, and then your enemy should threatening protagonist important things. This threat could be personal, practical or theoretical. The main character and the enemy are basically against each other. they should be enemies, otherwise emotion in your story drops and audience has no interest to watch it