Is this even going to work?
What is going to keep the Q3 (and thus Q1B) energized once you release the ON button? The base of Q3 will be floating when both switches are off. That will make the Q3 stop conducting (no base current) and Q1B will stop conducting as well because of that R3 resistor.
Also why R9 and R10? What is the purpose of those two resistors? First, they could be combined into one, second, they don't do anything but dump about 300uA to ground when the device is on.
I also can't say that I like the design with the TL431CP. That is a voltage reference, but there is no comparator anywhere. All you have is the threshold voltage of Q1A - which varies from part to part, changes with temperature, etc. That doesn't make for repeatable and robust design. There is no hysteresis neither, so your circuit is likely to oscillate right around the threshold voltage (the first FET will NOT turn off, so everything is powered, the battery recovers a bit, the second FET turns load on, the voltage drops again, the load is turned off, lather-rinse-repeat ...)
The calibration with the trimpot - what if someone drops your gizmo (it is meant to be portable, right?) and the pot moves? Boom goes the battery when the thing doesn't turn off ... You don't want this to be adjustable.
Also exceeding that threshold voltage does not ensure that the transistor will be fully conducting (it only starts to conduct - you need a lot more Vgs to open it fully!), so you are likely going to be producing a lot of heat in that FET.
I suggest you take a step back and do a bit of research on how others have implemented these things. I would also completely separate the on/off circuit and the safety cutoff. Their role is different and like this you are only likely to compromise the function of one or the other. Or both. Especially considering that the battery cutoff circuit could be easily part of the battery pack itself, as it is commonly done.
BTW, this topic has been discussed here several times already and the threads did include links to both circuit ideas and parts you may want to use:
https://www.eevblog.com/forum/projects/3-7-lipo-undervoltage-protection/https://www.eevblog.com/forum/beginners/i-need-to-find-a-good-low-voltage-cutoff-circuit-for-lipo-batteries/https://www.eevblog.com/forum/beginners/latching-'off'-circuit-lipo-cutoff/ etc ..