Why would Alice not tell Betty she was working with the FBI?

Especially when Betty had her tied up in the bunker for days trying to un brainwash her. Why wouldn't she come clean and explain it to her then? its not like Betty would blow her cover. Plus she burned all their personal photos in a fire looking all crazy, why do that if you're not really brainwashed?

Thats like the one big thing that didn't make sense in the finale, Alice not telling Betty what she was really doing. I mean your daughter was being traumatized by this shit, breaking down and crying over you joining them and nearly dying, and you still kept up the lie? seriously?

I honestly think her being an FBI informant was a last minute change for the finale because of all the backlash of fans saying how they ruined Alice, because as i said it makes no sense that she wouldn't tell Betty what she was doing. I truly think her being an FBI informant was never planned and just added for the finale as a quick way to redeem Alice and make fans happy with her.