When I go to update from IOS 9.3.5 it says my ipad is up to date, yet the apps are requesting IOS 10. or higher. My Ipad is model A1395 - can I upgrade?

Your very old first generation iPad2 can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).

Apple ended update support for iPad2 in September 2016. Your iPad2 cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed; the iPad2 is a 32-bit architecture device, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms. iPad2 is effectively obsolete.

You may wish to consider that compatible Apps for your iPad are increasingly difficult to find - as third-party developers are increasingly dropping support for older versions of iOS preceding iOS11/12/13. As older versions of Apps are removed from the Apple App Store, you’ll not be able to (re)download or install them - which may severely limit the usefulness and utility of your iPad if you should you ever need reset or restore your iPad. As such, if you want or need to access most current Apps, requiring more recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model.

Of current models, even the entry-level iPad7/8 has specifications and capabilities that will massively outperform you current iPad - and is compatible with the vast majority of current Apps. Other models are more powerful still.

I hope this information provides helpful and succinct clarity as to your available options - and the limitations of your current iPad.

iOS 10 is not installable on iPad 2.

No, there is not a way to update an iPad 2 to iOS 10. Your only solution is to buy a newer iPad.