Your question is difficult to answer because there are so many variables. There are some studies that show that the children of mothers with schizophrenia tend to fare better than children whose mothers have other disorders such as depression, but the research is mixed.
There are several possible reasons why one child would fare better than others. Let’s use depression as an example. It may be that individuals with depression tend to withdraw and be isolative. Children are egocentric. If a mother is withdrawn and thus not interacting with her children, the child may take it personally, as though it were the child’s fault. The child may misinterpret the mother’s behavior to mean that their mother does not want to be with them. They may feel unloved or unwanted. No parent would intend for their children to feel this way but that can be the outcome.
Alternatively, the nature of schizophrenia is quite different than that of depression. Individuals with schizophrenia may become withdrawn but many do not; it would depend on the type of schizophrenia. A mother who is behaving bizarrely is not likely to be withdrawn or isolative. She may be psychotic, but this would not prohibit her from interacting with her children. The children may not be fully aware that their mother is psychotic and therefore don’t necessarily view her behavior as being a major problem.
Anecdotally, I have worked with families who have reported that when their schizophrenic mother would become “sick” (i.e., be in the midst of a psychotic/schizophrenic episode) she would become fun and gregarious. Her personality would shift from wanting to spend an “average” amount of time with her children to never wanting to leave their presence. From the children’s perspective, they see this change as positive.
It could have been that when your mother was psychotic she was still able to function in a way that did not negatively affect or interfere with her parenting abilities. In addition, if there were siblings in the home, then these relationships could have buffered any negative impact. Another possibility is that when your mother became “sick” the family would grow closer together. Any one of these possibilities could have insulated you from being negatively impacted by your mother’s illness. Count your blessings because not everyone is so fortunate.
I hope this helps to answer your question. You may want to read the work of Diane Marsh. She has done a great deal of research on the effects of children with mentally ill parents. Please take care.