There are so many stories such as yours here on the forum of strange problems and issues that are caused by an weak, old or worn out 12V aux battery.
i suspect that the grabby brakes on the second press of the pedal occurs with a weak aux. When the pedal is first pressed it causes spooling of the actuator motor forward to increase the hydraulic pressure, but then when the pedal is released there is not enough voltage left in the system (aux + big black capacitor) to drive the motor back to the home position. When the pedal is pressed the second time the hydraulic system is already highly pressurized such that even the smallest pedal travel causes a massive lock on the calipers.
One test of this might be to remove the fuse for the capacitor and test drive the braking action.
Replacing the aux battery is the same as for an ICE car, remove negative terminal first, then positive. Install positive first, then negative.