My eye liner doesn't seem to budge when I double cleanse. I tend to use Clinique TDDO balm as a first cleanse followed by a avene ultra gentle milk or whatever it is. Both removed with warm damp muslin.
I often find I need to do the first step twice! My skin isn't loving all the (gentle!) manual exfoliation.
Ive largely stripped back my routine but not getting this right.
I've found I need to bloody scrub if I use Micellar water as a first step so that's not the answer. 
