charging a 11.1V lithium ion battery pack while connecting to arduino

My charger is a smart charger that has 4V to 16V auto-detection with 1 A.

This confuses me. I use several different LiPo chargers and this spec does not ring any bells.
Can you post a link to that charger?

If you have access to mains power to run the charger, why not simply use mains to run a power supply?

Another possible solution - get 2 batteries. Run off of one until it is low. Swap batteries. Connect the one that was just swapped out to the charger and charge. Repeat.