This is a known problem... I've had it happen to 6-8 ipads over the years that were in iPort wall docks.

Apple apparently implemented a software fix for this is an update sometime last year.

Apple was swapping the swollen iPads for what I think was a $100 flat rate.  I used this service to replace several of them, but that was at least a year ago so not sure if the service is still available.  I think they even replaced some for free (out of warranty) based on the serial number.

Edit: Check this link and scroll down to battery replacement ($99):
[Link: support.apple.com]