my mother and father separated when i was a boy but never divorced. he died; can my mother petition my half siblings?

Hypothetically, there is a presumption that any child born to the parties during a marriage is, in fact, a child of the marriage. However, a legal separation would most likely rebutt that presumption. If a wife, separated from a husband for anumber of years saught custody of the husband's children by another woman, it is likely that a court would find she did not have standing to file a custody petition, and deny her request, unless truely extraordinary circumstances could be shown. A half sibling of such children would have a much better chance of prevailing on a custody petition.