That is really something you should discuss with your GP or endo. Popcorn has quite a lot of carbs (50g/100g for butter, 80g/100g for sweet according to carbs&cals), so I think you'd need extra insulin for any more than 15g carbs.
Unfortunately, serving sizes vary and staff are unlikely to know the weight of the popcorn (never mind carbs) so that further complicates things - a guesstimate would be 25g-90g depending on serving size; if you want to be sure, buy some popcorn today, weigh it at home and take her to the cinama tomorrow or buy packaged popcorn and explain to staff that she can't have the popcorn at the cinema unless they can provide per serving nutritional information.
At the end of the day, there is no fundamental difference between the popcorn you have at the cinema and the dinner you eat at home - there is no magical excuse for not injecting insulin for the popcorn.
You might start by looking how much carbs your daughter has for dinner (fixed insulin doses implies fixed meal sizes), and then work out how much insulin she would need for the popcorn. If she usually had 50g carbs for dinner, and the popcorn was a small serving with 25g carbs then you'd give half the dose, etc.
Finally, I would assume that your daughter wants to go to the cinema to watch a movie, and would probably enjoy going to the cinema without popcorn more than not going at all, and you will probably have explained already that she can't eat randomly throughout the day because of diabetes. Tell her that you will talk to the doctor about how she can have popcorn next time.