how does my child sign in

Good. I had no clue you were asking about your childs device. I'm glad it's working now.

Now do yourself a major favor. Write down her Apple ID, Password and Passcode somewhere safe for quick reference. In Screen Time, make it impossible for her to make account changes.

iPad is not a multi-user device. If you want to sign in and out of accounts, you will create a massive nightmare for yourself.

Perhaps look at a discounted, refurbished iPad from the Apple Refurbished store and give your child their own iPad, which you can use Family Sharing on and Parental Controls to managed content and usage.

https://www.apple.com/shop/refurbished?afid=p238%7CN6VpWOYK-dc_mtid_1870765e38482_pcrid_78065330702666_pgrid_2053191222_&cid=aos-us-kwbi-brand--slid---apple+refurbished+store-be-product-

LOL......that's a VERY important one.