I strongly believe that Scorpius did not end up in Slytherin.
JK Rowling plays with the theme of people and ideas that change throughout the entire book. In Deathly Hallows, each change that the characters undergo is for the better. We see Peter Pettigrew and his moment of remorse that saved Harry’s life, Ron’s new maturity that eventually leads him to destroy a Horcrux (and helps him get Hermione as well), Severus Snape’s ultimate redemption... I do not think that the Malfoy family can continue in the same vicious pureblood mania circle anymore.
Although I do believe that Lucius Malfoy might still stick doggedly to the pureblood doctrine, I think that Draco is now beyond that. Doubts on the life he led as a Death Eater’s son and a Death Eater would definitely had been born in him on the night he couldn’t kill Dumbledore. But he is a coward and would have tried to hide these doubts in front of Voldemort and his father.
And then we have the fact that Harry saves his life once, and that Ron does again. After that, I feel it is impossible for Draco to continue hating muggleborns and blood traitors. And then when the war is over, what does he have to hide? He can finally come out and be somewhat tolerant. He might still contain some slight prejudices, but full-out detestation? I don’t think so.
Scorpius, as Draco’s son, is born free. He lives in a world free of Voldemort, where the tension between muggleborns and purebloods is now minimal. Draco, I think, would try to let Scorpius become what he wants to be, even if he does not necessarily encourage him towards one side or another. Scorpius is the first of a line of “new Malfoys”. It would be such a shame to waste this by making him a stereotypically Slytherin, pureblood snob.
I believe it is very likely Scorpius ended up in Ravenclaw. This, for a pureblood Slytherin family, would not be such a shock than if he were put in Hufflepuff or Gryffindor. It would represent a baby step forwards for the Malfoy family.
As for the relationship with the Trio’s children…I think there might be some conflict when they are young and immature, but this would eventually bloom into a cool respect. There would definitely be some tension if Draco and Harry/Ron had to meet up because of this, though…
I must say though, when I read this quote from Deathly Hallows:
I thought oh boy, let the ships begin! Quite frankly, I do not think there is anything “far-out” about Scorpius and Rose, because the whole point of Scorpius is that he is a free character. He can be whatever he wants to be, good or evil, he can do whatever he wants to do.'So that's little Scorpius,' said Ron under his breath. ‘Make sure you beat him in every test, Rosie. Thank God you inherited your mother's brains.'
Beth: Very good post. 5 points