My interpretation was that it was about more than just idea that he cared for his family. It was also about him (and Carmela) trying to, in some way justify their lifestyle choices by trying to make sure their kids were raised well and became successful. Look how Tony was so set on the idea of Meadow becoming a doctor. They wanted to brag and make sure their kids successes make them look like good people. I can easily see a guy like Tony justifying his life in his head by telling himself everything he's done was worth it because he provided for his kids and his daughter will hopefully go to medical school. Almost like trying to make up for his bad by making sure the kids do good. Of course a lot of parents do this or have that sort of mentality. A lot of it seemed to come down to his own selfish insecurities. This even becomes more clear in one of the last episodes where Tony is telling Dr. Melfi how much nicer it would've been had Meadow went on to be "Dr.Sorpano" and Dr. Melfi has a look of disgust.

All the while, he actually wasn't such a great father because he lived a lifestyle in which any day could be his last day of freedom, while risking life in prison or an early death. His children knew this as they got older which would add trauma and anxiety knowing their father is living such a risky and dangerous life.