Power supply or-ing with ideal diodes - priorities?
So let me try to describe what I’ve come up with. First of all, here’s an overview of the functionality of the LM66100: It compares the voltage at the !CE pin to VIN. If the voltage at !CE is higher than at VIN, the LM66100 disables its VOUT. If the voltage at the !CE pin is lower than VIN, it switches VIN through to VOUT via its internal MOSFET. Additionally, the ST pin outputs the status of the device: When the device is turned on, ST is High-Z, when the device is off, ST is pulled low.
Now to the reasoning behind my circuit:


The !CE series resistors R19, R21, R23 are current-limiting resistors in case of reversed polarity, as recommended by the data sheet

Let’s start with VBAT=4V, VEXT=0V, USB_VBUS = 0V. Since U5’s and U6’s ST are low, U7’s !CE is low and VINT is powered through U7 by VBAT.

Now VEXT comes on with 4.2V (it’s maximum). Since U6’s !CE is driven low by U5 via R25, VINT is powered through U6 by VEXT. U6’s ST goes HIGH-Z, U5’s ST is still low, weakly pulling U6’s and U7’s !CE low. But VEXT is pulling U7’s !CE high via D6 and R18, so U7 turns off and VBAT is disconnected from VINT. Diode D6 prevents VEXT from back-driving USB_VBUS.

Now USB_VBUS comes on (5V). VEXT can never drive U5’s !CE pin to a higher voltage than USB_VBUS, so U4 turns on and connects VINT to USB_VBUS. U5 lets go of it’s ST output, and also, U6’s !CE is driven high by USB_VBUS via D5, R17 and R21, and with U6’s !CE now being higher than it’s VIN, it disconnects VBAT from VINT. Diode D6 prevents USB_VBUS back-driving VEXT via R22 and R23.


This is proven to work in my application now, so I removed my feedback request and updated the schematic.