SS8550 isn't a MOSFET, and if you try to use it as-if it is, Q1 would dump 12V onto USB Vbus as soon as you plug in the cable, probably killing the host, or at least blowing the host port!
Assuming you replace it with a P-MOSFET as shown by schematic symbol, it wouldn't be likely to cut off 12 V power, as to do so it would need a gate threshold voltage in excess of 7 V, and to be wired with its source to the positive power source, otherwise its body diode would bypass it!
The next MOSFET, switched by MAIN_PWR, is also ineffective due to its body diode polarity.
Q2 should function as designed. Note that CHG_OFF must swing rail-to-rail, i.e. about 12V at this point. However the TP4057 charger IC has Abs.Max. Vin of 6.5 V so will fail if you enable charging with the 12V source supplying power, and may take the battery with it, explosively!