What fault codes are you getting? If anything, disconnecting the battery to charge it may clear the fault codes (but really should note what they are first). If your car starts now, disconnecting and charging can't stop it starting.
As for the battery, 2years doesn't sound too bad considering I agree with Husky's info there. The normal batteries do not like loosing charge, this greatly reduces their life. So with a life expectancy of 3-5years, being hard on it in regards to depleting its charge, 2yrs doesn't sound that odd. If the charge of your battery is going to be run down often, a deep cycle battery should be used. Or a battery that will be drained down a long way.
So personally, if I drove my car in those conditions I would firstly check the alternator for peace of mind. At least see what voltage it is charging at, just remember in the VE it is a variable rate. Mine will charge as high as 15.1V but as low as 13.?? V (that I've seen). Then I would either buy a charger wired into the car to make it easier than removing it all the time, buy a deep cycle battery and charge it less (or take a longer drive every other weekend should charge enough), or get used to buying a new battery every 2 years or so.
PS- if you've got a smart phone, I'd buy one of those cheap OBD2 dongles off ebay (think I paid $15ish). That way you can monitor the charge rate of the alternator in real time (might help show if there is a problem). I use a bluetooth one as my phone is android, but iPhone's need wifi. USB is a better connection, but I don't know if using that will provide enough power to charge my phone at the same time so I keep mine charging through the usb and bluetooth the dongle.