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I agree with Tim: a 2A charger probably isn't going to be enough, but then that's a guess, not knowing how long you're actually using the car each day.
If you're forced to switch the alternator back on after drawing the battery too low, your mileage will plummet. I made that mistake once, and went from being able to achieve something like 75 mpg (driving with load) to just 50ish mpg with the alternator struggling to recharge the flat battery and run the car.
If you ever do find yourself in that situation, disconnect the additional battery so you're only recharging one. (I'm assuming you added one in parallel, rather than replaced the regular starting batt.)
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