It's heavily implied Gordon eventually found out with this one quote from Return of the Joker:
"We buried the Joker deep beneath Arkham, The only other person who knew what happened that night was my father, the first Commissioner Gordon. He promised to keep our secret." - Barbara Gordon
He had to have known after that. I don't think there was anyway around it. It was heavily implied in the episode "Over the Edge' that he knew Barbara was Batgirl anyway...
"Sweetheart, you're capable of making your own decisions. You don't need me to approve or even acknowledge them. And in this case, I can't. All you need to know is I love you. All of you. (kisses her) And that is all I have to say on the subject." - Jim Gordon
That whole incident at the run down Arkham with The Joker really fukked Bruce up. He sent Tim off to get help from Leslie Thompkins and forbid him from becoming Robin ever again, had a fall out with the Justice League, Bruce's wound from the knife in the knee fukked his leg up eventually, who knows how Alfred's health was doing during this time, and this incident haunted Bruce forever (as seen in "Epilogue" which is set a few decades after Batman Beyond).
When it rains, it pours. Even in death, The Joker won, brehs.