I was closer to my MIL than my own mother when the girls were born. My Mum also felt it was OK to fault-find during the "Early Parenting Years" when that stuff really niggles, whereas my MIL would support ME and not really pass comment on my girls.
Sadly she died far too early, but I now have a much more understanding relationship with my own mum. She came to her own "ah-ha" moment a couple of years ago. She told me that she had us in her twenties when there was not much money and certainly nowhere near the amount of activites, classes, groups that there are for kiddies these days. She said when she looked at my kitchen calendar, and the amount of running around mothers do these days, plus the fact I had babies in my forties, it made her head spin!
Why am I telling you all this? I guess I personally feel it is not so much about being the mum or the MIL, it is about a woman supporting another woman - if that makes sense?