As to whether someone with a child should be admitted--I guess that's the call of the individual organization. Like Lindz said, it would be frowned upon at the big Southern universities.
That being said, GLOs need to make sure that a PNM who's a parent clearly understands when a child can and can not be broght to group functions. Some people are totally dense about this and would bring a child to rush, formals, events with alcohol, and even initiation.