1997 Mercedes Benz E420 Rough Idiling

You don't have to remove the battery to charge it. In fact, that can result in a lot more problems. "Fuel trim" data stored in the Engine Computer will be lost. You rarely notice when that is being rebuilt, but it can take miles of driving for that to occur. There's a lot of computers on your car and you don't want to take the chance on one of them locking up requiring a trip to the dealer.

If the engine started without a jump-start, the battery is charged sufficiently, and it would already be mostly recharged after driving nine miles. The exception would be if there's a problem with the generator. You'd need a professional load-test to identify that.

If you do want to charge the battery, keep the charger on the lowest setting for about an hour. Higher current settings can damage an older battery.