Adding a second device for child on family sharing

When using Family Sharing you aren't adding devices you are adding Apple IDs. The child is already part of it and should be able to share on any device signed in under the child's Apple ID, with a 10 device limit per account.

Share App Store, iTunes Store, and Apple Books purchases with Family Sharing - Apple Support

""With Family Sharing, family members get immediate access to each others’ music, movies, TV shows, books, and apps, and can download them to their own devices any time they like." " Not all content and content types are available in all countries. To share purchased content, all family members must use the same iTunes Store country or region. Music, movies, TV shows, and books can be downloaded on up to 10 devices per account, five of which can be computers. Apps can be downloaded to any devices the family member owns or controls."

What only lists the ipad? You're seeing IDs not devices.

If you don't see your family's shared content - Apple Support

On your iPhone or iPod touch

1. If you're not signed in, sign in with your Apple ID.
2. Open the store app that you want to download content from, then go to the Purchased page.

• • iTunes Store: Tap  > Purchased.
  • Apple Books: Tap  or your photo in the upper-right corner.
  • App Store: Tap  or your photo in the upper-right corner, then tap Purchased.

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2. Tap your family member's name to see their content. Learn what to do if you don’t see any content or can't tap your family member.
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4. To download an item, tap  next to it.

Did you read this section of the article?

Add a device to the list

After you sign in on a device with your Apple ID, that device appears in the list. Here's where you need to sign in:

• For iOS 9 and later, sign in to iCloud, iMessage, FaceTime, the iTunes and App Store, or Game Center on the device. You can also see your paired Apple Watch.
• For iOS 8, sign in to iCloud or the iTunes and App Store on the device. You can also see your paired Apple Watch.
• For OS X Yosemite and later or Windows 10 and later, sign in to iCloud on the device. 
• For tvOS 7 and later, sign in to the iTunes and App Store on the device.
• If any of your devices are using earlier versions of iOS, OS X, or tvOS, you won’t see them in your device list.

Does it show on her device list?

Apple ID device list -Check to see where you‘re signed in

I'm also confused. My first reply asked if it was on her device list. The reply back was "It does not show the phone on the device list, only my phone and her iPad", which makes it sound like they are using the same Apple ID???

I guess I am confused. I thought the device list was for devices under a given Apple ID, but this started off with talking about somebody using Family Sharing which presumably would mean the child's device is under a different Apple ID and wouldn't appear on the parent's Apple ID device list. ???