From what I read, It sounds like your alternator is not charging. With it running you should have 13-14.5 volts comming from it. You have to have greater than 12 to charge a 12 volt battery. With low power of the batteries, this can make the running of the engine be rough. When you lost battery power the computer has been rebooted and has to learn all its settings over again. The injectors need plenty of power to operate correctly. I would fix the electrical problem and get every thing charged up or replace and see where you are then with the drivability problems.
Jim