Large language models are widely applied to creative writing tasks. Creative writing requires a balance between subjective writing quality (e.g., literariness and emotional expression) and objective constraint following (e.g., format requirements and word limits). Existing reinforcement learning methods struggle to balance these two aspects: single reward strategies fail to improve both abilities simultaneously, while fixed-weight mixed-reward methods lack the ability to adapt to different writing scenarios. To address this problem, we propose Reinforcement Learning with Mixed Rewards (RLMR), utilizing a dynamically mixed reward system from a writing reward model evaluating subjective writing quality and a constraint verification model assessing objective constraint following. The constraint following reward weight is adjusted dynamically according to the writing quality within sampled groups, ensuring that samples violating constraints get negative advantage in GRPO and thus penalized during training, which is the key innovation of this proposed method. We conduct automated and manual evaluations across diverse model families from 8B to 72B parameters. Additionally, we construct a real-world writing benchmark named WriteEval for comprehensive evaluation. Results illustrate that our method achieves consistent improvements in both instruction following (IFEval from 83.36\% to 86.65\%) and writing quality (72.75\% win rate in manual expert pairwise evaluations on WriteEval). To the best of our knowledge, RLMR is the first work to combine subjective preferences with objective verification in online RL training, providing an effective solution for multi-dimensional creative writing optimization.