It depends on where you are trying to get. This doesn't seem to be about trying to be a better person. The OP is new money and wants her children to grow up comfortable in certain social circles. This is separate from learning to be a nice confident person or other such things and OBVIOUSLY not more important. Those social skills and cultural knowledge are okay to be concerned with in addition to other aspects of teaching one's children.
I agree that the cultural knowledge OP is referring to is also nice to have and ok to teach kids (although I think I have different ideas than OP about what those things would be, to each their own). What I am getting at is that if you don't have basic interpersonal skills then the cultural knowlege and other "assets" won't do you much good as you just won't be invited to the party, so to speak. They just won't get you anywhere if you are kept on the "outside" because people just don't want to be around you.