LiOn batts don't use a straight line charger like other rechargeable batteries. In fact you could cause them to explode and/or catch on fire if you did! So the answer here is you need to use the correct charger & logic to charge your battery.
You can't externally recharge the battery as the battery is glued down so well you end up damaging it trying to remove it. You could put in a fresh battery in, thats your only option.
As to altering your iPad to use an external battery - Not needed as you can do that now with one of these: [http://lifehacker.com/five-best-external-battery-packs-509802431|LifeHacker.com - Five best external battery packs].