This paper proposes a novel multi-frame-based framework, MF-LPR$^2$, for license plate region restoration and recognition in dashcam videos, where accurate license plate recognition is difficult due to low resolution, motion blur, and flare. To address the problem that existing pre-trained models generate serious artifacts and distortions when restoring low-quality images, MF-LPR$^2$ resolves the ambiguity of low-quality images by aligning and aggregating neighboring frames instead of relying on pre-trained knowledge. We utilize a state-of-the-art optical flow estimator for accurate frame alignment and design an algorithm that leverages the spatiotemporal coherence of license plate image sequences to detect and correct incorrect optical flow estimates. Experimental results show that MF-LPR$^2$ significantly outperforms eight state-of-the-art restoration models in terms of PSNR, SSIM, and LPIPS, and achieves a recognition accuracy of 86.44%, outperforming both the best single-frame LPR (14.04%) and the best multi-frame LPR (82.55%) among 11 baseline models. We evaluated MF-LPR$^2$ by constructing a new Realistic LPR (RLPR) dataset.