Child feces are an important source of fecal exposure in household environments. Typically, one of two behaviors is necessary to mitigate this risk: either caregivers dispose of their children's feces into a latrine or children learn how to use a latrine. Although past studies have examined factors associated with these two behaviors collectively (i.e. "safe disposal"), there is a need to separately analyze these distinctive practices to better inform programming. This study aims to quantitatively examine contextual and psychosocial factors influencing caregiver safe disposal and, separately, child latrine training. We surveyed 791 primary female caregivers, who reported on 906 children <5 years old, across 74 villages in rural Odisha, India. At their last defecation event, 38% of children used the latrine and another 10% had their feces safely disposed of into the latrine. Since caregiver safe disposal was rare, we instead assessed safe disposal intention. We used linear regression and multilevel mixed effects models to examine contextual and psychosocial factors. For contextual factors, we found caregivers had stronger safe disposal intention when they came from wealthier households and had greater informational support, but weaker intention when their latrine was near the household. Caregivers more intensely practiced latrine training with their child when they themselves used the latrine for defecation, the latrine was fully intact, and they had greater instrumental support. For psychosocial factors, caregivers had stronger safe disposal intention when their households expected them to practice safe disposal, they felt strongly committed to the behavior, and had a plan for what to do when faced with a water shortage. Caregivers more intensely taught their child how to use the latrine when they believed their child was at risk of becoming sick if they practiced open defecation (OD); viewed child OD as unbeneficial; liked teaching their child; personally felt it was important for the child's father to help; felt confident in their ability to teach their child; and had greater action control over their training practice. Interestingly, caregivers put less effort into latrine training when they felt more concerned for their child's safety when the child defecated outside. These findings underscore the critical need to separately assess unique child feces management (CFM) practices and also provide a road map for practitioners on the types of behavior change strategies to consider in their CFM programming.