Unfortunately, you're off by one generation. The batteries for the 2nd and 3rd gen iPads have different part numbers, connectors, voltage, form factor, and vastly different mAh ratings. The 3rd and 4th gen iPads do use the same battery, but the 2nd and 3rd aren't interchangeable.
Gold star for attempted reuse, though!
Here's a link to iFixit's battery that's made for your 3rd gen.
[product|IF116-001-4|iPad 3/4 Battery - iFixit Store|new_window=true]
Good luck with your repair!