The only way to do this is to have Blank child slots already pre-configured for every user whether they have children or not.
Create a sheet Called children and create some Columns called Parent Email, Parent Name, Child1Name, Child1Pic, Child1Age, Child2Name, Child2Pic, Child2Age. For this example I have 2 child preconfigured for every user, with their childs name age and pic.
do a formula such as =Unique(Userssheet!A2:A) and place it in the “Parent Email” Column of the child sheet. This will automatically carry over all users to this sheet once they log in the app. (Of course you need to set the UsersSheet as the main login sheet.
Create a reference from the usersheet to the childsheets via relating the parents email. Now when indivdual is editing their profile you will have a link to edit the children information automatically on the other form without needing to submit the form.
So you would have a Live form in a form by link relationship.
Technically you are not “Adding a child” because you assume everyone will have a child and assign a blank child slot to everyone already. This way you don’t have to Submit a form for a child slot to be related to the parent. All your users are assumed to be parents and are reserved child slots. Now all that is left if for the real parents to just fill in the blank child slots according to whatever info you want them to fill out based on the child columns you setup.
Hope this helps. Its just a matter of thinking outside the box.