Charging battery through relais and arduino
Charging a lead-acid battery is a bit more complicated than your on-off switching logic, if you want to do it right. You'll have to provide constant current first, then constant voltage, and finally a pulsed charge in the end.

The main issue you may face with your schematic is when you start charging the battery after a deep discharge. Since you charge with constant voltage, that may result in high charge current, which may damage the battery itself, the relay and D2.