Older ipad 3rd gen iOS software update

If you are attempting to perform an "over-the-air" update, I suggest that you connect your iPad directly to a computer with iTunes or Finder (for macOS Catalina) and perform the update that way.

A 3rd generation iPad should be upgradeable to iOS 9.3.6. Are you saying that you were not able to do so with your iPad? If so, how were you going about upgrading and what exact error messages were you seeing?

FYI,

After the upgrade, you may find many, MANY older versions of the most popular, third party apps to be no longer available for download for that 8-year old iPad.

Third party app developers have moved their apps to, at least, iOS 11 and later, now and have removed all of their older iOS 10 and earlier older app versions from Apple’s iOS App Store.

So finding apps for that old an iPad, while still possible, currently, will be a challenge, now, in 2020.

One of the big thngs will be finding compatible games.

Games are first to disappear or become non-functional on older iOS devices.

You maybe able to still get kids books to read through the Apple iBooks app if that gets installed with iOS 9.

Depending on how old your children are, you may find some simple drawing and coloring book style apps still available, but older version game apps are going to be problematic in 2020.

Just letting you know what you are going to be in for using an 8-year old device that hasn't been supported by Apple in well over 3-1/2 years!

Good Luck to You!