Can I swap a Battlefield from Brush and then exhaust Green Father to make it a Brush again?

Yes, you can swap a battlefield back to its original state and subsequently place a Brush battlefield token on it using Green Father, provided the specific conditions for each ability are met.

Explanation and Breakdown

1. Swapping the Brush Back: According to the text of the Brush battlefield token, when you score at that battlefield, you have the option to replace the Brush token with the original battlefield. This is a one-time choice triggered by the act of scoring.
2. Using Green Father's Ability: According to the card data for Green Father, its ability allows you to replace battlefields with the Brush token when you play the card.
3. The Interaction: Once the Brush token has been replaced by the original battlefield, the Brush token is removed. If you meet the requirements specified on Green Father's card, you may trigger its ability to replace the battlefield with a new Brush battlefield token.

Important Timing and Rule Constraints

• Scoring Limits: You can only score at a given battlefield once per turn. If you swap the Brush back by scoring, you have already used your scoring opportunity for that battlefield for the turn.
• Ability Trigger: Green Father’s ability is tied to the specific event of playing the card; you must perform the action that satisfies the trigger condition as outlined in the card text.
• Chain Timing: When the condition is met, the ability enters the chain as a pending item. You and your opponent have the opportunity to react to this ability before it resolves and replaces the battlefield.

Note: I could not fully verify this ruling against the retrieved rules.