Do you think relationship of parents plays part in children's personality?

Most definitely. Children are affected by what their parents do regardless of if they show it when they are children or when they have grown up. If a child's parents have a good relationship, married or apart, the child will grow up to have good relations. If the child lives in a one-parent home and that parent puts down the other parent, the child will think that is ok. Even when a child is old enough to know right from wrong, they still may copy their parents. It is just a natural way to act. Some people learn from others' mistakes, whereas, some may duplicate them.

I think it has alot to do with a child's personality also. They tend to act out by what they see also.

Definitely, relationship of parents plays a very significant role in children's personslity.If parents fight in front of children , it creates a very tense situation for the children and badly affects their personality development.Having differences infront of children also puts the children in a fix in deciding who is right and who is wrong.In consequense,it destroys the position of both parents as a role model in the minds of children.Result is children grow into a personality which is greately harmful to them as well as society.