The transversely partitioned dual-gain thick gas electron multiplier (DG-THGEM) can provide different effective gains for the beam region and the recoil region within the same detector, enabling wide-dynamic-range readout for online heavy-ion beam dose monitoring. However, under low-pressure hydrogen and strong-ionization conditions, high-energy δ-electron escape reduces the primary charge-collection efficiency, while ion backflow (IBF) exacerbates electric-field distortion in the drift region. These effects jointly limit gain stability and narrow the available operating window, necessitating a quantitative assessment of the constraints imposed by δ-electron transport and IBF suppression on DG-THGEM operation. In this study, 185 MeV/u ¹³²Xe is used as a representative heavy-ion beam. Geant4 is employed to calculate the spatial energy-deposition distribution, the 95% cumulative radius (r₉₅), and the δ-electron escape fraction in low-pressure hydrogen. Meanwhile, COMSOL Multiphysics is used to solve the periodic electric field of the THGEM hole array, and the resulting field map is imported into Garfield++ to simulate electron drift, transport through the holes, and avalanche multiplication. By scanning the reduced field (E/p), the drift field, the voltage across the THGEM holes, and the induction field, the quantitative relationships among electron transparency, effective gain, and IBF are systematically established, and the available operating region of the DG-THGEM is evaluated under the combined constraint of δ-electron escape and ion backflow. The results show that, with increasing gas pressure, the δ-electron range decreases significantly, leading to a reduced escape fraction, which becomes approximately 14.7% at 60-80 kPa. Within this pressure interval, the radial spread of deposited energy is also better confined, indicating improved primary charge retention. Simulations of electron transport and multiplication further demonstrate that gain allocation plays a decisive role in IBF suppression. By shifting the main multiplication stage to the second THGEM and simultaneously increasing the induction field, the IBF can be reduced from about 50% to 5% while maintaining an effective gain of 2000 and an electron transparency of approximately 85%. These results demonstrate that the DG-THGEM can achieve a favorable balance among charge collection, gain, and ion suppression in low-pressure hydrogen. This work provides a quantitative simulation framework for evaluating the coupled effects of δ-electron escape and ion backflow in DG-THGEM detectors under intense heavy-ion irradiation. The identified operating window and gain-allocation strategy offer practical guidance for the design and optimization of DG-THGEM-based detectors for online heavy-ion beam monitoring and dosimetry.