low side current sense
Hi, charge current will drop if the battery reaches full capacity. Because of this it will be necessary to provide power to the load from an other supply. If you don't do this, the load will clamp the battery voltage at a voltage of say 3.5V. Not that much below 3.6V, but your battery will be charged for 80% at 3.5V. So, basically it will require two current sense resistors. I would go for high side current sensing based on a ZXCT1009. This devices can be switched off by disconnecting the Iout pin with a BC807 or something alike.
Regards