Power adapter output is 10W - a USB on a pc between 100w- 500mw upto 1w typical. A car charger is somewhere inbetween, Do you know what the quoted output is for your device. The effective nominal output will also depend on how well constructed the charger is - a faulty or poor performing alternator on your car will also affect performance due to ripple on the supply. An output of around 5.1V at 2.1 amp is comparable with the mains unit.
There is nothing wrong with your iPad. What you have described would be normal behavior for the way you are using your iPad. New iPad has a battery twice the size of iPad 2 to power the faster processor for the amazing retina display. This uses much more juice than iPad 2. So, when using it and trying to charge by a lower watt charger than a wall charger, you will see the battery go down.
That is normal behavior. I use my iPad while it is plugged into the wall socket with the power adapter and it will charge slowly, but the absolute best way to charge the battery is to plug it into a wall socket with the power adapter and just let it charge overnight.
Your lighter port in the car and the USB port on the Mac just do not supply enough power to charge the device efficiently while it is being used.
Read this for the instructions for the proper care and charging of the battery.