Automated Market Makers (AMMs) are essential to decentralized finance, offering continuous liquidity and enabling intermediary-free trading on blockchains. However, participants in AMMs are vulnerable to Maximal Extractable Value (MEV) exploitation. Users face threats such as front-running, back-running, and sandwich attacks, while liquidity providers (LPs) incur the loss-versus-rebalancing (LVR). In this paper, we introduce RediSwap, a novel AMM designed to capture MEV at the application level and refund it fairly among users and liquidity providers. At its core, RediSwap features an MEV-redistribution mechanism that manages arbitrage opportunities within the AMM pool. We formalize the mechanism design problem and the desired game-theoretical properties. A central insight underpinning our mechanism is the interpretation of the maximal MEV value as the sum of LVR and individual user losses. We prove that our mechanism is incentive-compatible and Sybil-proof, and demonstrate that it is easy for arbitrageurs to participate. We empirically compared RediSwap with existing solutions by replaying historical AMM trades. Our results suggest that RediSwap can achieve better execution than UniswapX in 89% of trades and reduce LPs' loss to under 0.5% of the original LVR in most cases.