I'd play it all by ear. If you get a late discharge then sure it might make sense not you have your older child waiting there since rocking the boat right before bedtime isn't a great idea. Otherwise it should be fine to have your kid come home the same day as you if you want that.
I was discharged in the morning (maybe around 10?). We went home and my daughter came home around 4:00 pm I'm not a romantic person so I had no desire to have my first night be anything other than practical. You'll be a family of 4 for LONG time, waiting for one or two extra nights for everyone to be together won't have much impact one way or the other.