We need to understand the following few things for choosing the right IC for reset.
1)We have two sources for input power to processor. one is 5V input from wall adapter or USB interface and second one is Li-ion battery.
Li-ion battery is charged from processor so if we need to charge the battery processor should be up and not in reset.
As we have two power sources 5V (at 4.3V) and battery (at 3.2V) which have different brownout so we need to take care both situations.
Case 1: when 5V is applied and battery voltage is above 3.2V: No need to reset the processor as processor has sufficient input voltage from battery.
Case 2: when 5V is applied but battery voltage is less than 3.2V: As battery voltage was low than threshold and reset need to be provided fro 5V source.
2)We also need to know if we need to physically disconnect the battery in case battery voltage goes below threshold and at what voltage.
3)what to do with the battery in case battery voltage goes below the threshold voltage ( if we need to disconnect it ). We can also discuss with him for probable battery disconnection circuit if it needed.