Resistor or no resistor between this IC and the pmos GATE?
Open the datasheet of the ADM1270 and scroll to page 14 and look at the Typical Application  circuit:



I do not see any gate resistors.

A quick search in the text also makes no mention of gate resistors.

The typical application where gate resistors are needed are in fast switching applications like DCDC converters. There a gate resistor can help prevent current spikes by limiting the current to the gate and making the on/off transistions a bit slower.

This ADM1270 is not continously switching, in fact, in normal operation it doesn't switch at all as long as the input voltage and current don't exceed a certain value.

So the MOSFETs aren't used in a way that a gate resistor is needed. Chances are that the IC will already limit the gate current to a safe value anyway.

So no: gate resistors aren't needed.