From the pic your posted,your alternator isnt fully charging your battery!12.9 v even at idle is very low (I see 13.5v on mine and 13.7 thereon).
Still I have reason not to trust the OBD volt nr.9 volt display!Today ,it was showing 12,0 v,when I stopped engine ,yet when I checked the voltage in the engine compartment with my multimeter,it showed 12.32 v...which is quite a dfference.
There are a lot threads here on this subject but they are still not conclusive!Simplest way to check a battery voltage is with a cheap multimeter.Best way is to check the crank amps but this involves a more expensive conductance tester.
If you get hold of a multimeter ,first thing you should do is,disconnect battery from the car (remove terminal cables) ,fully charge it and check the voltage thereafter.Fully charged it should read 12,60 (make sure you take a reading after about 10 minutes of charging,thus allowing battery to settle).Check voltage again after about 3 hours and if battery has dropped to 12,4 or below ,then battery not holding charge and needs to be replaced.
If battery doesnt register a considerable drop ,then next thing you need to do is connect the + positive terminal and remove the - negative terminal.With your multimeter in the 10 amp section ,put the one prong in the battery - negative terminar and the other in the negative cable.Check the reading on your multimeter and it should be "0.00" ,,Anything over and you have a parasitic draw in the car,which you can find out (tediousy)by removing each fuse one by one until you find the one thats drawing amps (your multimeter will then show "0.00".
Additionaly,you can find someone with a battery conductance tester SOLAR BA5 100-1200 Cold Cranking Amps Electronic Battery Tester Brand New! | eBay
and check the crank amps.(this is a great way to check if battery has enough "juice" to start a car and easiest and quickest way to check a bad battery!I had batteries showing 13,0 volts but only 400 amp out of 900amp!

Hope it helps and let us know how you get on