Your diagram would work. The only things I would change is when charging your battery you may leave the main power on draining the battery while charging it. I'd try to prevent this by having to unplug the main feed to everything and plugging in the charging lead.. Also your LED's will need a resistor so it's better to start with higher voltage than what they need. I'd also tap this power off your 6v battery instead of using AA's.

Ryan