After the fiasco in Parshat Vayeishev that occurred to Joseph and his brothers because of that striped coat, you're probably thinking that I'm going to write about not showing favoritism among children, or perhaps about the need to treat all one's children exactly alike.
We learned from Yitzchak Avinu that we cannot treat each child the same. Perhaps if our Patriarch Yitzchak had given Esav a more appropriate education, sending him to archery school in the morning and then learning a little in the afternoon, all of human history would have been different. All children are different. They have to be educated differently, spoken to differently and simply raised differently. Even though children are raised in the same house, a parent is and must be a different person to each child, according to his needs.
This is something that I have learned from my Dearest Mother, ad 120. And she always says that she's heard the same from her long-time friend Rebbetzin Esther Jungreis.
I learned from my mother to treat each child as the most special, but to give to each what he particularly needs, and not necessarily the same thing as his brother. This is a parent's challenge, and it doesn't end when a child grows. It continues in even more complex ways. Combine this with the fact that one day IY"H if we are blessed, there are grandchildren who must also be treated uniquely and differently, and you see the role of a grandparent is even more complicated than that of a parent.
Forgetting the deeper meanings that we know come from the coat (i.e. each letter of Pasim stands for a terrible event in Joseph's life - Potifar, Socharim [merchants], Ishmaelim and Midianites), do I think that Yaakov should have given Yosef the striped coat? I don't know, but I'm willing to learn more about it.