After you have set up the Billing Data and the different Billing Plans in the "Configuration" subcategory of the "Billing" module, you can assign the plans to the different children.
In the "Billing" module, choose the "Billing plans" subcategory. All the children enrolled in your school are now listed in the middle. You can filter list by group or by billing plan.
Next to children's names you can see which plan they are following, when the invoice is due and when the last invoice was. At the right end is the details button. Once you click on it you'll get all the available billing plans listed on the left with a description on the right. You can also customize a billing plan for an individual child.
This way, billing will be made based on the Plan chosen by the parent, without any confusions.