Catastrophic forgetting is a significant challenge in deep reinforcement learning (RL). To address this problem, researchers introduce the experience replay (ER) concept to complement the training of a deep RL agent. However, the buffer size, experience selection, and experience retention strategies adopted for the ER can negatively affect the agent’s performance stability, especially for complex continuous state action problems. This paper investigates how to address the stability problem using an enhanced ER method that combines a replay policy network, a dual memory, and an alternating transition selection control (ATSC) mechanism. Two frameworks were designed: an experience replay optimisation via alternating transition selection control (ERO-ATSC) without a transition storage control (TSC) and an ERO-ATSC with a TSC. The first is a hybrid of experience replay optimisation (ERO) and dual-memory experience replay (DER) and the second, which has two versions of its kind, integrates a transition storage control (TSC) into the first framework. After comprehensive experimental evaluations of the frameworks on the pendulum-v0 environment and across multiple buffer sizes, retention strategies, and sampling ratios, the reward version of ERO-ATSC with a TSC exhibits superior performance over the first framework and other novel methods, such as the deep deterministic policy gradient (DDPG) and ERO.