Diffusion magnetic resonance imaging (dMRI) is essential for studying the microstructure of the developing fetal brain. However, fetal motion during scans and its interaction with magnetic field inhomo-geneities lead to amplified artifacts and data scattering, compromising the consistency of dMRI analysis. This work introduces HAITCH, a novel open-source framework for correcting and reconstructing high-angular resolution dMRI data from challenging fetal scans. Our multi-stage approach incorporates an optimized multi-shell design for increased information capture and motion tolerance, a blip-reversed dual-echo multi-shell acquisition for dynamic distortion correction, advanced motion correction for robust and model-free reconstruction, and outlier detection for improved reconstruction fidelity. Validation experiments on real fetal dMRI scans demonstrate significant improvements and accurate correction across diverse fetal ages and motion levels. HAITCH effectively removes artifacts and reconstructs high-fidelity dMRI data suitable for advanced diffusion modeling and tractography.