Recent technologies have extended opportunities for online dance learning by overcoming the limitations of space and time. However, dance teachers report that student-teacher interaction is more likely to be challenging in a distant and asynchronous learning environment than in a conventional dance class, such as a dance studio. To address this issue, we introduce DancingInside, an online dance learning system that encourages a beginner to learn dance by providing timely and sufficient feedback based on Teacher-AI cooperation. The proposed system incorporates an AI-based tutor agent (AI tutor, in short) that uses a 2D pose estimation approach to quantitatively estimate the similarity between a learner's and teacher's performance. We conducted a two-week user study with 11 students and 4 teachers. Our qualitative study results highlight that the AI tutor in DancingInside could support the reflection on a learner's practice and help the performance improvement with multimodal feedback resources. The interview results also reveal that the human teacher's role is essential in complementing the AI feedback. We discuss our design and suggest potential implications for future AI-supported cooperative dance learning systems.