My iPad software won't update

To amplify comments already made by Neil and Phil0124, your iPad2 cannot be updated beyond iOS 9.3.5 (for WiFi Only devices) and iOS 9.3.6 (WiFi & Cellular models).

Update Support for iPad2 was formally ended by Apple in September 2016. Update to later major versions of iOS are not possible - as iPad2 does not meet the minimum technical requirements for newer versions of iOS.

If you need or use Apps that require newer or current versions of iOS/iPadOS, you have no alternative other than to replace your current iPad with a more recent or current iPad model.

No, unless your unit is subject to the GPS issue which 9.3.6 patches; that version doesn't add any new functionality or do anything else.

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No. A second generation iPad is 9 year old hardware. It has reached the end of software support life cycle.

If you need iOS 10 or newer, you need a newer iPad.