Optimizing large language models (LLMs) for long-horizon caregiver agents requires balancing delayed task objectives with immediate environment dynamics, such as patient distress and resistance. In dementia care, this balance is especially difficult: trajectory level rewards are too sparse for turn level credit assignment, while external LLM-based evaluators are costly and can misread fragmented or indirect patient responses. To address this issue, we propose \textbf{T}urn-\textbf{T}rajectory \textbf{G}roup \textbf{R}elative \textbf{P}olicy \textbf{O}ptimization (\textbf{T$^{2}$-GRPO}), a framework that decouples caregiver RL into two normalized reward horizons and enforces safety through a binary hard veto. $T^2$-GRPO derives dense turn-level rewards directly from environment state transitions, measuring changes in patient distress and resistance from a frozen dementia patient simulator. These environment-grounded rewards are combined with trajectory-level evaluations through independent centered-rank normalization, which preserves heterogeneous reward signals and mitigates reward collapse. Extensive experiments on dementia caregivers show that T $^{2}$-GRPO outperforms competitive baselines, indicating a substantial improvement for emotionally sensitive caregiver scenarios that effectively handles immediate patient feedback, long-term care outcomes, and safety constraints.