Being the kid of a criminal in Gotham is no fun. Being the kid of a criminal in Gotham big name enough to get on the Bat Family's radar is even less fun. Being the kid of a criminal in Gotham big name enough to get on the Bat Family's radar when you are working with said Bat Family yourself...
Don't get Steph wrong, she's so, so proud of you. Overcoming a villainous lineage like that to make yourself into a hero instead? That's amazing. It's not easy. Heh, she should know, right? Two peas in a pod, the two of you, at least in this sense. Maybe you don't always get along, what family does, but when it comes to this? She gets it.
And the truth is, no matter how much you know it's the right thing, no matter how determined you are to stand against them, no matter how much you've dedicated yourself to atoning for their sins, having to be part of the mission that leads to the capture and arrest of your own parent really, really sucks. And she understands. Which is why, when you hang back a bit from following all the others back home after the mission, Spoiler hangs back with you. You didn't invite her to, but... well, sometimes people just shouldn't be left alone, y'know?
"Hey. ...You okay? That was kinda a lot."