As Mr.Corvette mentioned, a smart charger is recommended if your 2 amp isn't one already. A traditional trickle charger's output is continuous(which harms the battery over time), while a smart charger monitors and adjusts the voltage in steps, according to the state of charge. NOCO and CTEK are two of the best brands.
I highly recommend that you test the condition of your battery. By your description, it sounds like it may be failing. More than eight years old? Just change it. If battery tests good, check for parasitic draw. A good battery with minimal draw should keep it's charge for a month or two. You can test your battery with a relatively cheap battery tester. The Ancel BA101 Car Battery Tester is a good one for under $50 CAN. Or, if you prefer, take it out and bring it to service centre to have it tested.
If your battery is failing, it will be hard on the home charger and the car's charging system, if you run it this summer. The high resistance in the battery will cause the alternator to work harder and longer. It is just a matter of time before it fails outright...typically at the worst possible moment.
Hope this helps and have fun with the new ride!