I like the idea about moving some of the preview ads to the middle of the movie... as it is, I and my friends have got timing our arrival at the theatre just in time to buy tickets (the self-serve terminals are a huge boon for this), snacks and drinks, and find a seat just before Kevin Bacon appears exhorting us to turn our phones off. With less leeway, and a break in the middle, we'd be encouraged to turn up earlier (thus seeing more of the pre-roll ads), and maybe leave snackage until the middle if we had to skip it at the start (meaning greater revenue for the concession stand). Everybody wins.
Then again, it's been a very long time since I had to get up in the middle of a film anyway. The last one where I started really feeling an urge to walk around - because of posterior numbness rather than a full bladder - was The Hobbit, and its length is notable by its rarity. The last film I bothered with before that which nudged three hours was LOTR...
And there's a fair old problem of security, too (how are you supposed to double check people's tickets to let them back in, or be sure they're not sneaking out of one film into another? with the small trickle who may come out of a regular movie it's no problem, with a couple hundred coming out at an actual intermission it's far more challenging, you have to schedule them to not clash in the middle as well as at the start and end...) which encompasses fire safety and potential crushes as well as financial concerns - plus midpoint demands for refunds if they think the film sucks. If you're getting up anyway, then it's far less of a hassle to do that, when otherwise you might have just sat through it and lumped it.
I don't even think it's because of audience preference or advertising revenues, in fact. It might just be that the logistics of the whole affair would be unmanageable, particularly in a multiplex. A traditional theatre showing a stage play only has the one production to worry about, and a relatively long intermission in the middle of a long performance, with only two or maybe three "curtains" per day, so the start of act 2 can be briefly held up if not everyone has made their way back to their seats on schedule (...digitally fed cinemas can have almost completely automated projectors these days, no projectionist sat there changing reels who can keep an eye on things). An older, small fleapit cinema will only have between one and six screens, typically two to four, which is far easier to juggle. Multiplexes have no chance - but if enough places start doing it, regardless of size, they'll all be expected to.
There was an alternative approach I came up with however - show the movies in full in their first week, maybe two (depending on age range, length, and popularity), then switch to intermission showings after that. Beyond the opening weekend and maybe the week after it, theatres are rarely fully packed out with no seats to spare (even seeing ST:ID in the UK this weekend, on the third day of showing, I was able to easily get a seat for the earlier of two evening slots even as practically the last person to ask for one, more than fifteen minutes after the posted "start" (of trailers) time). Towards the end of the run, they can struggle to fill more than 10% of the seats. Having fewer showings per day, then, could potentially SAVE (or if you prefer, "make more") money for the theatre, as it's not exactly cheap in terms of electricity or materials to run a professional grade cineprojector. If you can do it fewer times but still fill as much time and get the same number of customers paying the same amount, perhaps preferentially so for longer films because they know there'll be a break and they otherwise would have waited for the DVD, then that's additional pure profit in your pocket. We already have differential showings with 2D vs 3D, regular vs IMAX, subtitled or audio-described, seniors / juniors matinees and the like, so why not "intermission" and "non-stop" as well?
BTW, the longest "kids" film I know of is roughly 2 hours... was made in the 80s... and stood out due to its length even then. But some of the others in the "longest kids films" top 10 were made in this decade. I don't think it's children's movies "these days" that are short, they're just short in general. You probably want to have the offer of a break at about the one-hour point (or halfway if they're shorter), if only because that's the sort of rhythm they may be used to from BBC or PBS programmes... (and every 30, 15 or even 10 minutes for BBC/PBS kids or anything on a commercial channel)