I wouldn't be too hard on the kids for sulking, either. When you're a teenager, it can be hard to know which social rules are real (as in, for everyone) and which are based on people assuming you're a delinquent-in-waiting. My high school boyfriend and I went on a long-awaited trip to an art museum once and ended up making a game out of figuring out what area the guard who followed us religiously everywhere was actually supposed to be covering. It was funny, but also annoying, since I knew adults wouldn't have had the same treatment.
That's also why my answer to whether another diner should have said something about it being normal is "yes." It might have been helpful to know they weren't being picked on specifically.
Per the bolded: actually, I had the same experience when I was in my early 30s. I had taken my older son to a small art museum. FTR, son didn't touch anything, I had him by the hand at all times, and we both behaved quite well. Still, a guard followed us from room to room (the reason it stood out was that at other times this hadn't happened). It was very uncomfortable. So, it may seem that teens are targeted but sometimes other people get it, too.
I have seen plenty of signs posted and "no backpack" rules around high schools and colleges, even limiting the number of students allowed in at a time in one or two stores. It's unfortunate these young people get targeted, but unfortunately, there is a reason why. I remember getting followed as a teen myself. I'm not sure what put me (and my friends) in the crosshairs, but there it was. I would really like to know what made Mom and Kid a target.
I remember being followed at stores when I was a teenager. I wasn't a shoplifter, but that didn't stop management from being suspicious. But I do understand that it's for a reason. I used to work as a retail merchandiser at several Walmart stores (its own circle of hell!). It was quite common for a shoplifter to be caught; sadly, a large number of them were under 21 yrs old, and many were parents (hiding things in their baby's stroller was common). But then I think of my late MIL, who was also a shoplifter. And it turns out that she was far from alone! Sadly, the younger people get targeted, not the seniors.
I did have one experience at a store in college that was such a turn-off that I've never been back - and that was over 30 yrs ago! It was Burlington Coat Factory, and my friends and I went into the store. A guard by the door went through our bags and purses, was quite rude, and made us feel like criminals. I have never stepped foot in another BCF again. Honestly, if he'd done his "check" with a better attitude, it wouldn't have felt so invasive. And, I didn't see him doing it with anyone else who came in the same time we did.
As for the guard in the art museum, it was just weird. This was a very small museum (compared to the Met in NYC, for example), and it catered to school groups. So that meant that kids were there a lot. My being there with one child was nothing compared to 30 elementary school kids w/2 chaperones. If it happened now, I'd stand up for myself and would speak with management (politely, of course).