In the prior episode. We saw Jacob driving to find Alice/Beth at the end of the last episode, confirming the one we saw in Gotham was fake.
Alice is trying to win the award for most stylish character on the show. In making her the "feminine" twin they've had her take away all of Kate's style points from the comics .
On top of that, no offense to the actress, but she's no Susana Thompson.I really feel like they were trying to pull a Moira Queen with Catherine, but it just didn't work. With Moira, we had almost two full seasons to get to know her, to lover her, to hate her, to see her complicated relationships with her children. So when she was killed, I was genuinely upset. But with Catherine, we've had, what, 7 episodes where we see she's a morally grey person who by inserting herself in the search for Beth ended up causing her to be held prisoner for 11 years and who's company makes WMD's and guns that can kill Batman (or Batwoman). And yes- her death is said, and I do feel sorry for both her and Mary, but I just don't feel it in the same way I felt Moira's death.
Alice is like Kate's Malcolm Merlyn .Not only didn't she accomplish anything, it can be argued that she indirectly caused Catherine's death and her father's incarceration by not informing the authorities as to where a wanted terrorist was hiding.
To be honest, I'm surprised they didn't say "you're under arrest for the murder of your wife" when they arrested him.To be fair, he probably just found out about Catherine's death not long before Kate came to visit him, and that's me assuming the cops told him when he was arrested. It's probably still sinking in.