Copenhagen to Gothenburg

You have two options: SJ High Speed trains and the Øresund trains.

Øresund trains - The most frequent and flexible option:
Interregional style trains. Frequent schedule with trains every hour or so. No catering onboard. Makes several stops in towns along the journey, so also used by commuters. Prices are fixed, and you don't have to book early. However their seat reservation system is suspended and will come back in "Spring 2025". Until then it's free seating for all.

SJ "Snabbtåg" / High Speed trains - The most comfortable option:
Higher comfort level (though I wouldn't call the Øresund trains uncomfortable). Less frequent schedule. Has a "bistro" onboard. Makes fewer stops, which is nice, but will probably require you to take an Øresund train to Malmö and transfer to the SJ train there. You can select specific seats on the SJ train when you book on their website. They use a dynamic pricing system as we know from airline tickets, and these trains can sell out. So book early to secure yourself a spot and get a low fare.

För Öresundståg the reservation system has been postponed two times so it might happen again. The Skånetrafiken app and ticket machines (only available at central station) will not offer seat reservation but it offers a group discount, a group ticket for 4 adults is 1504 SEK. 4 tickets with seat reservation will likely be 2484 SEK so very expensive. Since only half of the train is bookable (and only 25% of a long train) a trick could be to board at nørreport or østerport stations in Copenhagen (before the train reaches the central station) and grab an unbookable seat group, there is usually few passengers boarding before the central station so a high chance of success.

SJ offers very good discounts for kids.

No catering onboard.

But anyway it is a much better solution to buy a "picnic" at the station (or elsewere).

You get a much larger selection and the price is no higher. We have done this on trains in Denmark, Netherlands, Great Britain, Germany and Italy and enjoyed it every time. If you include a bottle of wine, remember to bring a corkscrew (if neccesary. But wine with a twist-off cap is much easier and the wine is just as good) and glasses (we prefer soft plastic glasses).

I've done a lot of those picnics and can confirm it's a good idea. Just worth noting that there's no onboard catering, as it would be less than ideal to be hungry and thirsty for the train ride.

If you include a bottle of wine, remember to bring a corkscrew (if neccesary. But wine with a twist-off cap is much easier and the wine is just as good) and glasses (we prefer soft plastic glasses)

Generally also a good idea, but not for this specific journey, as it's not allowed in Sweden. On the FAQ page under "Is there an onboard dining service?", Øresundstog writes: "There is no serving on board. You are welcome to bring your own food and drink. Please note that alcoholic beverages are not allowed to drink on board according to swedish law."

Go on the high-speed train. I always do. Just thinking about all the stops the Öresundståget commits to, before finally reaching Gothenburg makes me exhausted. There is always nice scenery though.

And you're also not allowed to drink alcohol on SJ's trains, unless you've bought it onboard. And I agree that you should go for the SJ train. It's usually a bit faster, even with the change in Malmö, and more comfortable. And if bought in advance, often cheaper. And while the bistro certainly won't win any Michelin stars, it's not that bad and the prices are reasonable. And it's nice to have the option onboard.