A 2011, 2nd gen iPad cannot be upgraded beyond iOS 9.3.5/9.3.6.
A 2nd gen iPad is a 9-year old device, now!
Its internal hardware is too old, underpowered and completely incompatible with any of the current and future versions of iOS/iPadOS.
Sorry. It is what it is at this very late date, now here in the year 2020.
If you need an iPad that can run the latest and greatest versions of iOS, as well as, the most current apps available, then, you need to purchase a new iPad from Apple or a discounted, refurbished iPad from Apple’s Refurbished & Clearance section of Apple’s Website or a new or refurbished iPad from an Apple authorised, third party retail or online reseller OR other trusted sources for new or used Apple products.
These old iPad 2, 3, 4 and 1st gen iPad Mini models are nearing 8 and 9-years old, now.
As of the beginning of 2019, many, MANY third party app developers are all more quickly and completely permanently dropping older app support for all old 7, 8 and 9-year iPads that are running 2-3 year old and earlier iOS versions ( iOS 10 and earlier ).
Third party app developers are removing all of their older, legacy versions of their apps from Apple's App Store servers, now.
Third party app developers no longer want to support these 8 and 9-year old or older iOS devices, any longer!
Older versions of apps are, soon, going to be gone for good, now!
Getting older versions of apps for these old iPad models, initially from Apple’s iOS App Store is getting very difficult and very problematic and this issue is getting, painfully, much worse in 2020, now!
These old iPads are now reaching their complete end of life and support.
So finding older versions apps for older iPads, while still possible, currently, will be a tough challenge, now, in 2020.
Old iPads that can no longer be upgraded/updated will have NO MORE APPS AVAILABLE for initial download, at all, soon, from the Apple iOS App Store, for such old iOS devices in the very near future.
Older versions of apps for these older iPads will be completely gone, at some point, in the very foreseeable future.
Again, it is what it is, today, in the year 2020!
So, this is really now the time to seriously consider a new or discounted, refurbished iPad from Apple or other Apple authorised resellers.
A lot has happened with iPad and iOS in 7-9 years and in the past 2 to 3-1/2 years since iOS 9 and 10.
As an example and compared to your 9-year old iPad 2nd gen,
The baseline 2019, 10.2 inch screen 7th gen iPads have a 1/2 inch larger retina screen, newer, more powerful and nearly 2-1/2 times faster 2.3 Ghz, A10 Fusion processors, AT LEAST, 3-4 times the internal RAM, with the 2019, 7th gen iPad having 3 GBs of internal RAM, iPadOS 13 support, with much better and improved multitasking features, Apple Pencil and Apple Smart keyboard cover support and have better audio speakers and better/improved built-in cameras.
Sorry & Best of Luck to You!
