You are right, there is an enormous amount of information out there to sort through. One reason that it is so difficult to find answers is that how the child will be affected by the situation depends on an large number of factors. This means that no amount of reading will give you a definitive answer about you nephew or niece's chances of doing well under your care. That is why consulting with your pediatrician
and/or pediatric psychiatrist
are very important steps. How the child will deal with being abandoned by a mother or father depends largely on the child's age at the time. The younger the child, the more likely that they will not be affected by this event. The older the child gets, the more they seem to fear additional abandonment. Probably the most common manifestation is an attachment disorder where the child becomes fearful and angry when the caregiver drops them off somewhere. Remarkably, most children are rather resilient and end up mentally fine in the end. I suggest you find a pediatrician for your niece or nephew that you feel you can easily talk to about any issues you see coming up. This way behaviors or mood changes can be recognized earlier and dealt with in an appropriate manner. Good luck.