You can set your child's iPhone to automatically and remotely backup to your iTunes on your local computer. The backup happens periodically when the phone and the computer are on the same wireless network and iTunes is running on the computer.
You can also request a manual backup at any time with iTunes.
Please also read the official Apple guide here:
Steps to Configure Automatic and Remote Backup to iTunes
1. Connect the phone to your computer using USB wire and open iTunes, this is needed only one time to set up the configuration,
2. Click on the device icon for the iPhone in the top-left of the iTunes window
3. Under the Backup section of the device summary, select “This computer” and ensure the checkbox for “Encrypt local backup” is left unchecked.
4. In the Options section select both checkboxes labeled "Automatically sync when this iPhone is connected" and "Sync with this iPhone over Wi-Fi". Click on Done button.
Now you will not need to connect your child's iPhone to iTunes on your computer to do a backup. It will be done automatically. You can also simply click on "Back Up Now" whenever your child's device is in the same Wi-Fi as your computer and your child's iPhone will perform a backup to iTunes on your computer remotely.
Family Orbit Desktop app performs a periodic check to see if new backup is available for the Apple devices you have selected to upload them to your private online panel. You can also perform a manual Sync from within the Family Orbit app.