I understand the answer is nr.2 and I understand the individual words, but what does にもつをだす actually *mean* here? Take out the luggage? Does she want him to like take bags of unused stuff and get rid of it? Like doing garbage disposal? If I was told 荷物を出してください I would assume I'm supposed to help someone get some luggage out of a closet or something, I don't understand how it's something I do on the way to the cinema?
The word "にもつ" typically means luggage, but it can also refer to packages. When the mother said "にもつを出してください," it literally translates to "take the package out." However, in this context, she actually wants her son to take the package and send it via the post office. In the conversation, she further clarifies by saying, "ゆうびんきょくによって、にもつをだしてくれない？", which means "Could you stop by the post office and send this package?" I hope this explanation makes sense.
I think he meant that he would stop by the book store afterwards (implying that it’s because he will bring the luggage to the post office beforehand). It was confusing for me too but I got it after listening a couple times. The mother also says after he says 後にするか “急ぎだから映画の前に行ってね” and he doesn’t contest it which I also assume means he will drop off the luggage beforehand like his mom asked.
Thanks for the answer. What you said is exactly correct. The mother is in hurry so he asked the son to drop the luggage before going to the cinema. When the son said 映画の後で, he referred to the 'going to a book store', which he planned to do it beforehand.
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