Diffusion tensor imaging (DTI) based group analysis has helped uncover the impact of white matter injuries in a wide range of studies involving subjects from preterm neonates to adults. The application of these methods to fetal cohorts, however, has been hampered by the challenging nature of in utero fetal DTI caused by unconstrained fetal motion, limited scan times, and limited signal-to-noise ratio. We present a framework that addresses these issues to systematically evaluate group differences in fetal cohorts. A motion-robust DTI computation approach with a new unbiased DTI template construction method is unified with kernel-regression in age and tensor-specific registration to normalize DTI volumes in an unbiased space. A robust statistical approach is used to map region-specific group differences to the medial representation of the tracts of interest. The proposed approach was applied and showed, for the first time, differences in local white matter fractional anisotropy based on in utero DTI of fetuses with congenital heart disease and age-matched healthy controls. This paper suggests the need for fetal-specific pipelines to be used for DTI-based group analysis involving fetal cohorts.