You can use the "Show/Hide" logic (feature in a Paid level subscription) to expose additional set/s of fields.
You can create the set of fields once and copy/paste the fields creating a second set (repeat as many times as you want to enable users to be able to add).
Also create the "Add child" field (could use a Checkbox field). You should include an "Add Child" field in the sets of Childs data fields you are copying and pasting if you want to expost 10-12 of those.
Select the second set of Child data fields (inculding the "Add Child" field so you can configure that one to show the 3rd set etc) and the "Properties" panel for the group of fields will have "Show/Hide" as an option (assuming the "View" setting from the View menu is "Web View"), select to Show/hide and in the Show/Hide dialog choose to Add a field and add the checkbox for "Add Child".
Repeat the steps above as many times as needed, the last group would not include the "Add Child" checkbox.
Whenever a user selects the "Add Child" checkbox another set of Child data input fields would be shown and another "Add child" box as well. You do need to create all of the possible input fields (meaning if you want users to be able to add up to 10 kids you would have to repeat this for 10 groups of fields).
Hopefully the steps are clear enough once you start to play with the Show/Hide fields logic.
Thanks Josh. I have taken your suggestions and completed the design of the form. Looks like all will work. Just need to thoroughly test it.
Again thanks for your time and help!!!