Sole custody is easy to enforce. One parent gets to do everything to the exclusion of the other parent. Enforcement is not an issue.
Under the circumstance you describe, joint legal custody, primary physical custody to mother, and visitation to the father may be fit your situation.
Joint legal custody allows both parents to have a say in how the child is raised. Primary physical custody recognizes the mother's better ability to watch the child. Visitation allows the father birthdays, holidays, etc.