Why not draw from only one battery initially, then take it out of circuit and connect the other one as soon as it drops to the minimum safe voltage (2.7V?). Relays (mechanical or solid state) or MOSFETS would likely be appropriate. A decent sized capacitor om the power supply would help to smooth out the transition.
With 2 batteries in parallel, there will be some danger of a reverse current in one of them, which will irrevocably destroy it.
Comparing the two batteries may not work too well. If they are connected in parallel a 0.5V difference will likely cause a reverse current in one of them. If one is connected, and one not, then the connected one's voltage will be lower as a result of the voltage drop due to internal resistance.
Charging in parallel does not seem like a great idea since each pack could have a different charge initially. The charging may terminate prematurely, or one pack could be overcharged, resulting in damage, or perhaps even overheating and a fire. Li-ion's are not very tolerant to abuse.