Discord is still essentially….. Discord.
Even though he now holds the title of "King" through his marriage to Celestia, it's just word. Politically, he's the equivalent of the First Lady to the President, and has no political power (Celestia made sure of that). Being a father has mellowed him out a bit, but he's still the prankster he's always been. After all, a couple decades is the blink of an eye to a being nearly as old as time itself.
Discord still likes to "mess" with ponies, usually wreaking havoc around them in order to teach them a very forced lesson (similar to what he did to Starlight in 'A Matter of Principals'), but now he likes to brag that these lessons are part of his duty as King (which they are, in fact, not).
Discord and Entropy have a rocky relationship. Entropy claiming that his dad is 'immature', and Discord saying Entropy has a stick up his butt. They butt heads from time to time, but Discord rarely takes it seriously, retorting with jokes and light sarcasm. Discord's lack of seriousness towards Entropy leads Entropy to distance himself further.
Solstice, on the other hand, is a chip off the old block. Although her sense of humor isn't quite as malicious, she loves teaming up with her dad and playing practical jokes on guards and on some rare occasions, Celestia (who always can appreciate a well-crafted prank).
Discord still meets up with Fluttershy as much as possible, and enjoys lending a hand at her animal sanctuary. He enjoys teasing Bulk Biceps by always threatening him that if he ever does anything to hurt Fluttershy, he will cause the buff pegasus to suffer immensely. Don't worry though, it's just a joke (probably).
His relationship with Celestia is all he could ever ask for, somebody who understands his humor. The two love to have pun battles, and enjoy playing various board games and doing puzzle montages.