On the basis that the only dumb question is the one you don't ask....

If the Detained character successfully clears the Detained condition with an Influence roll...does that roll replace both her actions, or can she take a second action at that point?

Detained is no different from other possible restrictions like not being able to perform Rest Action on a space with Monster.
If you get rid of the Monster (or move elsewhere) with your first action, then you can perform your second action as normal. (honoring other restrictions if any)
If you get rid of the Detained with your first action, then you can perform your second action as normal. (honoring other restrictions if any)