Why is the new battery not working as expected?

Did you calibrate the battery?

Lets get an idea on what your battery looks like now. Download this free app and take a screenshot of the main screen and paste it here so we can see whats up: CoconutBattery

I think you have a drain issue within the battery checker circuit. Did you ever spill some liquid on the keyboard at some point or sit your system down on a wet surface? I'm thinking you have some liquid damage either on the main logic board or the batter tester its self on the side is failing.

The easiest test is to disconnect the battery checker from the logic board to see if that speeds up the charging. Follow the first 3 steps in this guide MacBook Pro 13" Unibody Mid 2010 基板の交換 then jump down to Step15 to disconnect the battery checker, place a small piece of tape over the board connector and then reconnect the battery.

See if that changes things. If not You'll need to fully remove the logic board following the guide from the beginning so you can inspect the other side for liquid damage.