The Immigration and Nationality Act enumerates a variety of reasons that someone may be found "inadmissible" to the United States. However, an initial determination of inadmissibility is not always the end of the road when you're seeking entrance to the U.S.
Divorce is often a sad thing, as the husband and wife who once pledged to love and honor each other forever find themselves acrimoniously parting. Yet, despite whatever hard feelings they may have about each other, they need to do everything they can to make the divorce as constructive as possible for their children. Family law provides many opportunities for divorced parents to be mature enough to work together and put their children's best interests first.
Typically, family court judges want children to maintain a relationship with both of their parents after they separate or divorce, even if one parent is granted primary custody. Of course, if a parent is a danger emotionally and/or physically to the kids, that's another matter.