My DS (11) pretty much lives for "lazy days" where he's not expected to do, or participate in very much at all. Every other Saturday, he spends 9 hours with his father - and is run ragged. He's in school all week, with all that entails, and every other Sunday (on the opposite week to his time with his father) we spend the day with my side of his family. So for the "off" day in each weekend, he recharges his batteries. Actually, his paternal grandmother made him a birthday cake the other month with a little fondant DS lying in his bed, because she'd asked him what his best days were like and got the answer "being lazy!". He might well lounge about in his pyjamas, but he reads, draws, catches up on his homework, plays board games with me and his sister when she's not working.
When I was growing up, weekends were for pottering around and doing very little. By the time I became a parent almost 20 years ago, things had Changed (yes; with a capital 'C'!). Suddenly, we were failing as parents if our darling offspring weren't leaping around all hours of the day, doing ballet, or computing, or math tuition, or music lessons, or gymnastics, or dance classes, or... or... or...
My DS's friends mostly all leave school after an almost 7 hour day and go off to do another 3 or so hours of swimming/gymnastics/music/dance, they then have playdates, and homework, and... don't learn how to like their own company. They constantly complain of being bored - and their parents (with whom I'm friends) constantly moan about their whinging children. My DS doesn't moan, or whinge, or even whine about being bored. Because he knows how to entertain himself. Just as I did at his age. Actually, one of his closest friends has recently started coming to ours after school for tea... and being dropped off at his home at 7pm, but only on Mondays because the rest of the week is choc-full of "activities". And when he's dropped home? Well, it's then homework, and French lesson prep for the next night, and... why?! He's 10 years old, for crying out loud.
My 19 year old DD... well, I bought into the clap-trap until I realised too late the precedent that was being set. She now cannot occupy herself at all (has to be told what to do and when, often in great detail), panics if her days are not fully structured by other people, and has already "burned out" three times in the last 8 years. She's not the only one in her peer group. Actually, the only two in her immediate circle of friends who hasn't had some form of a breakdown, are the ones whose parents eschewed militant "they must be occupied/entertained 24/7" behaviour. Conversely, my DS is able to work out how to entertain himself. I've never been an emotionally absent parent - actually, it's possible they'd both insist that I'm too emotionally involved in what goes on in their lives. I work from home, but always with an ear and one eye to what is going on if they're around. I just believe in allowing my DS to be the child that I stupidly believed the hype concerning my DD not being.
Let your children get bored, OP. One day, I promise you, you'll be glad they were... because it teaches them to think for themselves, develop an independence that will stand them in good stead, and they'll be the best problem solvers you've ever met.
As for your mother... yeah: she's shit stirring. But then, if there's no shit to stir, she cannot stir the shit, can she now?!