You have 3 templates available for use on the Children's subsite: Index Children, Page Children (Subpage Default), and Page Full Width Chidlren.

Because the templates are duplicated from your main site, everything should work similarly to how you're used to them working. There are link lists specific to the children's site that control the footer links, the social links, and the home page featured links that you can edit by going to Content > Link Lists in the CMS:

You will want to use the children's templates for any pages on that site so that the navigation works properly.