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I think you can do that with payments as well.
Here are my recommendations.
1. This is not related with the payment but rather the information you are gathering from your students. If you will be collecting each information for each undefined number of children, this widget will be of help. http://widgets.jotform.com/widget/configurable_list. Parents can easily add more fields dynamically within your form to fill in the information of their child.
2. With regards to the payment, you can use any of the payment tools I have replied from your other thread. Then add a number quantity in your items or products e.g. number of children to be registered so it is multiplied by the base price. Here's how to add options in your products http://www.jotform.com/help/225-How-To-Add-Options-In-The-Payment-Form.
Let us know if you need further help. Thank you!