This in the context of a stage play. So his 'hard away' is him exiting the stage, but rather harshly. He doesn't want Harry to embarrass him or show him up at the station, so he leaves quickly.

Hey there, I would like to explain it accordingly to my understanding, Make a hard away means "a way of doing something that makes it more difficult than it needs to be" So it seems like he didn't want Harry to drop him to station as some children don't like parents to drops them so he feel embarrassed that's how he picked up his things and case in away it looks like he is doing it harshly or carrying them in a way looks little difficult.

hard = strongly, assertively, possibly aggressively . Explanation of why is given in Molly's answer.