By the time my DH and I married, his older brother had been married for over a decade. My SIL always called our MIL "mum-in-law", so I followed suit. Until my MIL asked me to call her "mum", which I did. I never figured out whether she disliked the actual title of MIL, or whether she wanted to have a different relationship with me as opposed to her other DIL (who's a bit bossy).
Anyway, it didn't seem strange for me to call her "mum" because although she was a bit difficult to handle at times (especially over my first-born, her first GC) she wasn't a self-centred bitch as my own mother could be.
Actually, now I think about it, overall those titles of DM and MIL were actually reversed in my case. My M was my mother by law as she gave birth to me, but my MIL was the one who valued me (not solely because I gave birth to her only grandchildren) and encouraged me when I went to university in my thirties (my mother never referred to that). My PIL thought my children were the greatest things ever to walk the earth; my mother never had any photographs of my children on display.
Whenever I read problem MIL threads here, it's my (D)M that comes to mind.
Gosh, I went a bit off-topic there. I'd forgotten how much it hurt. (They're both deceased now.)