In real-world scenarios such as e-commerce platforms and smart-home systems, multiple users often share the same account, resulting in behavioral sequences that mix interactions from different users. Sequential recommendation in shared-account settings has recently attracted increasing research attention but still faces two major challenges: (1) interactions from different latent users are difficult to disentangle accurately, leading to biased representation learning; (2) reliance on static hyperparameters to estimate the number of latent users prevents adaptive determination of user cardinality, which may cause underfitting or introduce noise. To address these challenges, this study proposes PE-GAT (prompt-enhanced graph attention network), an adaptive sequential recommendation framework for shared-account settings. PE-GAT first employs a dynamically-weighted, density-based clustering algorithm to infer the number of latent users and construct user-level sequential graphs that explicitly separate heterogeneous user behaviors. Based on these graphs, a graph attention network pre-training module is employed to disentangle mixed user preferences and learn initial sequence representations. Inspired by the pre-training and prompt-tuning paradigm, a self-attention-based prompt-enhancement module is then designed to refine sequence embeddings via prompt templates during retraining. Finally, account-level representations are fused with prompt-enhanced sequence embeddings to generate personalized recommendations. Extensive experiments on two real-world shared-account datasets (HVIDEO-E and HVIDEO-V) show that PE-GAT outperforms 14 state-of-the-art baselines, achieving maximum improvements of 4.73% and 5.59% in MRR and Recall metrics, respectively.