IDK what a Suzuki Swift is but I can try to help where I can.
I run two batteries in my Dodge ram truck. They are both acid celled 1000 CA / 850 CCA batteries and are under the hood. My stock alt is 136A. When I added my second battery I took the (-) and grounded it to the engine block and frame. I used a battery isolator to separate the batteries. It has three posts on it. One goes to the (+) of the main battery. The second goes to the (+) of the second battery and the last post goes to a switched (+) power source. So when the key is on the battery isolator allows both batteries to be used and charged. But when the key is off the batteries are separate and my power hungry toys rub off my second battery.
I have never had a problem jumping anything off but my setup may be bigger than yours?