bq76940 REGOUT problem while charging

It sounds like either a grounding problem or noise from the charger.

Check for ground differences in the system.  The EV2300 operates from USB 5V and is tied to the computer ground.  The 3.3V pull ups for the SMBus lines come from the EV2300. The EV2300 should operate without the bq78350, a communications adapter message may indicate a loss of power rather than noise on the REGOUT.   The low side protection switching of the bq769x0 simple implementation makes ground isolation important, with high side switching isolation is still important but the effect is more likely odd current reports from bypassing the sense resistor rather than large potential differences.

It may be your charger does not like a load.  You might check it with various loads. Also test your board with a power supply.  Note many power supplies are switching supplies and may have a frequency ripple in their output. 

Also look for sensitivities in your design to the charger to noise.  Check your layout for loops in the circuitry if you have not used a ground plane on the board.  A ground plane will normally give better noise performance.  Check for capacitor placement on the board, these are best near the IC pins, the VC5X, VC10X, BAT, REGSRC and REGOUT on the bq76940, also the capacitor across the bq78350 VCC to VSS.  Check the frequency response of the capacitors at the frequency of the charger, it may be beneficial to add small capacitors with low impedance at high frequency across the appropriate power pins.