Nope, it is not "OK" for a mother to take her child's food away without asking permission first. This isn't a matter of parental authority - it is general politeness.
Let's say you were eating with a married couple. The wife orders an appetizer, and when it arrives, as she starts to take a mouthful, her husband grabs the plate and asks, "Does anyone want some of my wife's appetizers?" Would you not think, at a minimum, he is being rude to her, in not at least asking, "Hey, can we share those?"
If the family tradition is to share appetizers, it does not spare the mother from the minimal common courtesy to her child to ask, "Hey, can we have some?" Basic politeness requires you to ask such a question, even if the expected answer is "yes, of course".
We have an "appetizers are to be shared family", so your scenario above would be fine with me. No, more than fine; it would be expected. My kids are always welcome to order an appetizer if they want one, but they know it's for the whole table. There would not need to be a discussion because that's the way we've always done it.
I don't think that we can know, without knowing if child in question comes from an "apps are to be shared" family, if the mom was rude or not. Nor do I think we should try to read anything into her facial expression.
In that situation I would expect the wife to pick up her plate and ask if anyone wants some of her appetizer. If her husband did it I would be making some uncharitable assumptions about him.
You will think what you will, but he would not be rude. Not in my family, and not in many others. If this were my husband and I, I would be the rude one for forgetting to offer the app to the others at the table.
If that is your rule then I would expect him to gently nudge you with a "hey can I have that" or something similar to remind you of the rule. but to just take a plate from in front of someone and offer it to others strikes me as boorish and controlling and I would be watching the relationship more closely to see if I should be offering any extra help. This would also go if the wife offered the husband's food.
Seriously. If a husband grabbed his wife's app and offered it to the table, I'd immediately look to her. If she indicated, by facial expression or otherwise, that she was fully supportive of the offer, I'd think it was a joint decision. But if she looked weirded out, surprised, or remotely upset, I'd assume he was being a jerk.
And if my SO and I had a perpetual understanding of 'apps are always shared with groups', and one day we were with a group and he seemed to be hogging the app he ordered, the most I would do would be nudge him and say softly, "want to put that in the middle?". I would never, in a million years, just grab it from in front of him and offer it myself when it looked like he wasn't going to. It feels incredibly disrespectful.