If I have a Miss Fortune at a battlefield and a Hidden Tide Turner at that same battlefield and my opponent attempts to charm my Miss Fortune off the battlefield, if I reveal my Tide Turner as a reaction to the charm does that allow me to move my Miss Fortune back to the battlefield?

No, you cannot use Tideturner to move Miss Fortune back to the battlefield after she has been moved by Charm.

If you wait for Charm to resolve and move Miss Fortune, you lose control of the battlefield (assuming she was your only unit there and it is not contested). Once you lose control, the hidden Tideturner is trashed during the cleanup step that immediately follows the movement.

Why this interaction fails:

1. Timing: Tideturner must be revealed and played as a Reaction to the Charm spell while it is still on the chain. If you allow Charm to resolve, the movement occurs, you lose control of the battlefield, and the Tideturner is removed from the game during the cleanup step (Rule 424.3.c and FAQ 1943).
2. Targeting Restriction: Even if you react in time, Tideturner cannot target Miss Fortune while she is at the same battlefield as the Tideturner. Tideturner's ability explicitly requires you to choose a unit at "another location" (FAQ 7937). You cannot use Tideturner to swap with a unit at its own location.

The Correct Sequence (if you react to Charm):

If you choose to use Tideturner as a reaction to Charm, you must do so before Charm resolves:

1. Opponent plays Charm: They target your Miss Fortune at Battlefield A.
2. You respond: You reveal and play Tideturner from hidden at Battlefield A as a Reaction.
3. Chain resolves: Tideturner enters play. Its "When you play me" ability triggers.
4. Targeting: You must choose a friendly unit at another location (Battlefield B). You cannot target Miss Fortune at Battlefield A.
5. Swap: Tideturner moves to Battlefield B, and the unit at Battlefield B moves to Battlefield A.
6. Charm resolves: Charm attempts to move Miss Fortune from Battlefield A. Since she is still at Battlefield A, Charm successfully moves her to a new location.

Summary: Because Tideturner cannot target a unit at its own location, it cannot be used to "save" or "swap" with a unit that is currently at the same battlefield. Furthermore, you cannot wait for Charm to resolve before acting, as the hidden card will be trashed before you have another opportunity to play it.