To improve the information exchange rate between Alice and Bob in traditional two-way directional modulation (TWDM) network, a new double-reconfigurable intelligent surface (RIS)-aided TWDM network is proposed. To achieve the low-complexity transmitter design, two analytical precoders, one closed-form method of adjusting the RIS phase-shifting matrices, and semi-iterative power allocation (PA) strategy of maximizing secrecy sum rate (SSR) are proposed. First, the geometric parallelogram (GPG) criterion is employed to give the phase-shifting matrices of RISs. Then, two precoders, called maximizing singular value (Max-SV) and maximizing signal-to-leakage-noise ratio (Max-SLNR), are proposed to enhance the SSR. Evenly, the maximizing SSR PA with hybrid iterative closed-form (HICF) is further proposed to improve the SSR and derived to be one root of a sixth-order polynomial computed by: (1) the Newton-Raphson algorithm is repeated twice to reduce the order of the polynomial from six to four; (2) the remaining four feasible solutions can be directly obtained by the Ferrari's method. Simulation results show that using the proposed Max-SV and Max-SLNR, the proposed GPG makes a significant SSR improvement over random phase and no RIS. Given GPG, the proposed Max-SV outperforms the proposed leakage for small-scale or medium-scale RIS. Particularly, the proposed HICF PA stragey shows about ten percent performance gain over equal PA.