In this paper, an intelligent reflecting surface (IRS)-and-unmanned aerial vehicle (UAV)-assisted two-way amplify-and-forward (AF) relay network in maritime Internet of Things (IoT) is proposed, where ship1 ($\text{S}_1$) and ship2 ($\text{S}_2$) can be viewed as data collecting centers. To enhance the message exchange rate between $\text{S}_1$ and $\text{S}_2$, a problem of maximizing minimum rate is cast, where the variables, namely AF relay beamforming matrix and IRS phase shifts of two time slots, need to be optimized. To achieve a maximum rate, a low-complexity alternately iterative (AI) scheme based on zero forcing and successive convex approximation (LC-ZF-SCA) algorithm is presented. To obtain a significant rate enhancement, a high-performance AI method based on one step, semidefinite programming and penalty SCA (ONS-SDP-PSCA) is proposed. Simulation results show that by the proposed LC-ZF-SCA and ONS-SDP-PSCA methods, the rate of the IRS-and-UAV-assisted AF relay network surpass those of with random phase and only AF relay networks. Moreover, ONS-SDP-PSCA perform better than LC-ZF-SCA in aspect of rate.