Running Angry Birds 2 on my iPads
The fact that the newer iPad is still prompting about an old account indicates it was likely never reset after the transfer of ownership.  Even when giving a device to a trusted family member, wiping is always a good idea; the new owner likely doesn't need or want any of the older owner's data.  Wiping it will also likely resolve the issues you're experiencing--and even if it doesn't, it will dramatically narrow down the cause.
The caveat is that by wiping it, you will be removing all of your data from the device.  You should back up anything important first.  If your daughter has already been using the device, it may be difficult to guess what needs to be backed up.  Some data, such as game saves, may not be reasonable to back up and restore after wiping.
If you decide to go through with wiping it, follow Apple's latest instructions; they tend to change across iOS versions.  As of writing, the process looks roughly like this:

Make sure your device is up-to-date.
Make sure you've backed up anything you want to save and have a plan for restoring it to the device--I recommend using both a cloud backup and an offline backup via your computer.  If the iCloud account on the device is the previous owner's, then keep in mind that you will lose access to any iCloud backups when you wipe the device.
&quot;Go to Settings &gt; [your name] &gt; Find My, tap Find My iPhone, then turn it off.&quot;  This is important.  Note that [your name] may actually be the previous owner's name.  As of writing, this option is usually at the very top of the Settings page.  It's possible that the device isn't connected to anyone's iCloud account, in which case you'll likely see a prompt to log into iCloud in its place.
&quot;Tap Settings &gt; General &gt; Reset&quot;, then tap &quot;Erase All Content and Settings&quot;