Oh, this'll get me in trouble, but I have taken my DD to normal showings of Kids films. She's 2.6 - and we've been doing it a while.
Now, we never go in the first week when it's likely to be packed, and we pick latish evening showings so she's tired and likely to want to cuddle. We pick seats and film times carefully - always isolated on the booking screen (and we wait till the last minute to buy them to be sure) or on one of the little blocks on the far side of one of the aisles, so there's no-one too close. And always as close to the door as possible, so I can haul her out without disturbing people is I have to.
We take her blanket, and ply her with food and drink, and by ten minutes in, she's usually sat on my knee, watching the thing and absolutely quiet.
Yes, she moves, occasionally, from me to her Dad - but who honestly sits completely still for two hours? - and occasionally, she'll ask me for something - in a whisper. Other than that, she's good as gold.
I would take her out of a film that she didn't gel with. I have, the once it happened, and quickly - I am aware that other people didn't come to be annoyed by her.
The thing is, the one time I tried the Kidsam thing, it drove me nuts. The behaviour of some of the parents - not the kids, who were being kids - was awful - no control, no discipline and half the time they were talking, at full volume. Too, DD's behaviour was much worse because she kept being distracted and she couldn't watch the film. So I won't be doing that again.
I'm aware she (and we) might be odd in this respect, but she sits, she watches, she's not disruptive, we pay for her seat (and ours), it's a film aimed at Kids and she enjoys it. Why shouldn't she be there?
I don't think OP was being unreasonable. As long as her child wasn't shouting, jumping up and down, throwing food or crying all the time, she did nothing wrong.