The requirement needed for college students to stay on their parent's health insurance was once dependent on keeping a full schedule in your college courses. With the passage of the Affordable care Act, also known as the ACA or Obamacare, the rules regarding health insurance have changed, and today your only requirements are to be within a certain age, and maintain your residence either in the parental home or at the college you attend.
There are some exceptions and waivers to this law, and many insurance companies still have minimum course attendance requirements, but a majority of insurers have already adopted the new rules for students and their parent's health insurance. Check with your parents' insurance company or your state Department of Insurance to find out whether the company you are insured by follows the new law yet or when they will be changing over.
The requirement allowing children to stay on the parent's health insurance applies to their dependents as well. For example, if your daughter gets married and them both live in your home, they and their children, if any, can also qualify for coverage. The requirement is simply that they must be 26 years old or younger, live at the residence, and not qualify for insurance through another insurance plan.
The law does not apply to situations where the parents are covered under a government sponsored health plan such as Medicaid or Medicare. In that case, you are only covered under their insurance until you reach the age of 18, you will have to reapply for the coverage on your own after that.
As a student, you are probably covered until the age of 26, without any requirements for minimum credit hours. To find out for certain, only the insurance company can tell you for sure, so you will have to talk with their customer service department to get the final say.