Your photo illustrates a broken third-party Lightning connector.
The photo shows that the entire end of the Lightning plug (that has retaining detents) is missing from the remains of the plug connector. As such, it is highly likely that this missing section of the plug is securely held (by retaining springs) within the Lightning port of your iPad. This would explain why you are unable to insert a replacement cable in your iPad.
You would be best advised to take your iPad to the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP), where the technicians will be able to offer assistance. If a broken plug is retained as described, specialist tools will be required to remove the damaged plug without causing damage.
Genius Bar Reservation and Apple Support Options - Apple
Many third-party Lightning cables are not MFI -certified - and breakage is not uncommon.