In this paper, the adoption of an intelligent reflecting surface (IRS) for multiple single-antenna source terminal (ST)-DT pairs in two-hop networks is investigated. Different from the previous studies on IRS that merely focused on tuning the reflection coefficient of all the reflection elements at IRS, in this paper, we consider the true reflection resource management. Specifically, the true reflection resource management can be realized via trigger module selection based on our proposed IRS architecture that all the reflection elements are partially controlled by multiple parallel switches of controller. As the number of reflection elements increases, the true reflection resource management will become urgently needed in this context, which is due to the non-ignorable energy consumption. Moreover, the proposed modular architecture of IRS is designed to make the reflection elements part independent and controllable. As such, our goal is to maximize the minimum signal-to-interference-plus-noise ratio (SINR) at DTs via a joint trigger module subset selection, transmit power allocation of STs, and the corresponding passive beamforming of the trigger modules, subject to per ST power budgets and module size constraint. Whereas this problem is NP-hard due to the module size constraint, to deal with it, we transform the hard module size constraint into the group sparse constraint by introducing the mixed row block norm, which yields a suitable semidefinite relaxation. Additionally, the parallel alternating direction method of multipliers (PADMM) is proposed to identify the trigger module subset, and then subsequently the transmit power allocation and passive beamforming can be obtained by solving the original minimum SINR maximization problem without the group sparse constraint via partial linearization for generalized fractional programs.