Yes, I think schools should be much more aware of family relationships when it comes to their students. Today's definition of a "family" is much different from the definition ten years ago. Today's children could have same sex parents, step parents, adoptive parents, foster parents, or single parents. Each of these situations can affect a child in many different ways so it is necessary for schools today to be aware of a child's home relationship.
Yes, family relationships should be given more attention by schools, because there is so much abuse that happens and schools just look the other way. Students are expected to perform in school, but the teachers do not care about the many children who are hurting in bad situations at home.
Every single family has problems. Schools are there to teach students. If they want to incorporate better moral value into a family, they should start by creating great children that parents can be proud of. After you have kids, a lot of problem start up because of them. Raising a great child will mean avoiding problems when they are older.
I do not believe family relationships should be given more attention by schools. Schools are in place to provide an education to students and the schools should remain loyal to those students. They shouldn't attempt to overreach their boundaries. Schools can barely provide the education they're suppose to, they shouldn't become concerned with family relationships.