I think if she's lying (to cover her own butt) then punishing her will create more scenarios for her to cover her own butt which will cause more lying.
The kind of punishment you are asking about does not teach children that they should be honest because it is the right thing to do. It teaches her to lie better so she doesnt' get caught.
I think you need to work on the root issue as well. The interrogation sounded scary and it's probably not fair to put the younger daughter in the middle.
We don't know you and only you know if you are being too strict or not. Lying is a very bad thing I think we all agree with that. Just trying to help change the behavior rather than make it worse.
I hope that didn't sound judgmental! Good luck!
