A dad who left it to the mother to raise the kids after a divorce is commonly referred to as a "non-custodial" or "absentee" father. This means that while the father may still have visitation rights or some level of involvement in the children's lives, the primary responsibility for raising and caring for the kids falls on the mother, who is usually designated as the custodial parent.
It's important to note that every family's situation is unique, and the roles and responsibilities of parents can vary depending on individual circumstances, custody agreements, and the best interests of the children. In some cases, the father's limited involvement may be a result of factors beyond their control, while in other situations, it may be a choice they make. Regardless of the circumstances, the well-being and support of the children should always be a top priority in any divorce or separation.