That was very good, hon. I get a feeling that Draco lives his life in tension -- that at the end of the war he was left in limbo, neither one thing nor the other, neither villain nor hero. For the rest of his life he's walking a tightrope and has to take each step carefull or fall off. Or at least, that's what he believes. So he still has the anti-mudblood attitudes but he has to watch himself to keep from passing them on to his son because he knows that's not a good idea now. Or at least, it's not politic, not conducive to getting ahead, and he's enough of a Slytherin not to sabotage his son's chances of getting ahead with of out-of-favor attitudes and thought patterns.
It's probably a pretty stressful and depressing way to live one's life, but then Draco wasn't exactly one of the good guys. Although one could also make the argument that he was a minor acting in the way he'd been taught was proper and right, and therefore in a way was also a victim of the situation. But still, I imagine Draco lives a fairly dull life of quiet stress and frustrated regret. Having Scorpius fit in and be accepted and do well is probably something he hangs onto with both hands.
Which is all probably more than you intended to be read into this piece [duck] but it made me think. Good job. :)