Recovering iPad with broken home button

There is NO solution.

With a broken Home button and a disbled iPad, that iPad will stay a dead and useless device without a means of device and data recovery.

The Home button is needed for many iOS/iPadOS emergency functions.

That iPad maybe too old too and/or too expensive for repair.

If a fairly recent iPad model, but NO paid, extended AppleCare+, device replacement will, also, be very expensive.

If a fairly old iPad, it will not be cost effective for any type of repair.

Very Sorry, but that iPad is dead/done.

Again, you do not state how old this iPad is, but if you decide to find some qualified third party repair shop that is knowledgeable in actually repairing Apple iPads, the Home button may be able to be fixed and an attempted recovery of your iPad would be possible and its recovery of its data may be possible, but is not a certainty.

But, at least your iPad would be working properly again.

Depending on the age of this iPad, If just replced through an Apple Store, Apple store may only offer device replacement without any chance of data recovery.

You many need to use the “Support” link, in the top black menu bar, at the upper right hand corner of every Apple Support Community Webpage to attempt to schedule an appointment with your nearest Apple Store location.

Apple Store employees will be glad to help/assist you.

Best of Luck to You!

It is a common misconception that an iPad (or iPhone) can remain fully functional with damaged or defective physical buttons. 

Whilst Accessibility features (such as assistive touch) can be used to augment the User Interface, these features cannot be used as a substitute for physical button sequences that must be used to trigger system recovery actions. Sooner or later, as now, you will encounter a situation from which you cannot recover.

Until repaired, you will not be able to resolve a locked-out (disabled) iPad - or reset a forgotten device passcode.

Repair or replacement of internal hardware, such as the Home Button, will effectively erase all stored data.

For hardware repair of eligible devices, Apple usually offer exchange for a reconditioned/renewed iPad of the same model and specification. As such, there will be no opportunity to recover data from the damaged device.

As is, unless your have a pre-existing backup of locally stored data, your locally stored data and files have been put beyond reach - and are unrecoverable.