WARNING: The following article contains spoilers for Batman: Three Jokers #3, by Geoff Johns, Jason Fabok, Brad Anderson, and Rob Leigh, on sale now.
Batman: Three Jokers #3, the finale to the long-anticipated miniseries, is predictably full of major revelations about the identities of the Jokers, Batman's motivations, and the fate of Red Hood, among other things. But it also delivers a big surprise about Barbara Gordon, Batgirl, and her relationship with her father Commissioner Jim Gordon, but it does so in a teasing. subtle manner.
At the end of the issue, as Batman turns the last remaining Joker over to police custody Barbara shares a brief moment with Jason Todd, in which they awkwardly discuss the romantic moment they shared in the last issue. After Jason leaves, Commissioner Gordon comes over to check on Batgirl. He assures her that "You have my support, as much as Batman does," before going on to say, "but Red Hood... He isn't someone you should be involved with." Barbara curtly replies, "What I do with him isn't your business… Dad," hinting at her her secret identity to her father with a wry reply.
Jim Gordon's knowledge, or lack thereof, of his daughter's double life is a constantly shifting element of DC continuity. In some universes, he knows who Barbara is but remains unaware of the identities of the rest of the Bat-Family, while in others knowing that Barbara is Batgirl has led him to discover who they all are. In a few select realities, he still has no idea who any of them are.
Jason Fabok previously explained how the creative team decided to keep Three Jokers in something of a loose continuity, leaving it up to reader and editorial response to determine if it would influence other stories in the main DC universe. Back in Three Jokers #1, Barbara told Batman that Jim doesn't know she's Batgirl, but Jim's own words suggest that he may have already deduced who she was. His concern for Batgirl certainly makes the most sense if he knew she was his daughter, although it could also be explained by his generally compassionate nature and friendship with the Bat-family.
One element of the issue that definitely does draw off of recent Batgirl continuity is the tension between Barbara and her father. Barbara is clearly annoyed by Jim's attempt to control her personal relationship with Jason and the moment feels similar to recent instances in the Batgirl solo series of her finding Jim to be overprotective. Barbara might also see a degree of unintentional sexism in Jim's paternalistic attitude. After all, he almost certainly wouldn't try to tell Batman how to handle his personal life, so it wouldn't be fair to do so to Batgirl unless he knew of their deeper personal connection, and probably not even then.
It's hard to discern exactly why Barbara would choose to reveal herself in this manner if that is indeed what she intended to do here. If Jim has secretly known who she is for a while, it might just be a way of acknowledging the elephant in the room. But the decision seems to signal some kind of shift in their relationship.
Thinking optimistically, it could be the case that the traumatic events of the series caused her to realize she needs a stronger support system and that being honest with her father is a part of that. But her frustration in the scene might also suggest that she told him because she knows the secret will cause conflict between them, suggesting that she might be going down an unhealthy road of self-isolation. Whatever her motives, the decision is sure to cause some major changes in the Gordon family.