I will be travelling with my 21 year old daughter at the end of July. We will be staying with a friend in Malmö for 3-4 nights, with side trips to Lund, and to Louisiana Gallery. Our last two nights are in Copenhagen. We have 3 days free in the middle. I am debating between Aarhus and Gothenburg.
Any advice?
This year? I'd say you need to book your accommodations ASAP, which could well decide the issue for you. Without knowing anything about you or your daughter (other than her age), it's impossible to make a recommendation. OTOH, why not stay the extra nights in Copenhagen and move your day trip to Louisiana to that stay? More time with your friend in Malmo or another day trip within Sweden. There is plenty of to see and do in Copenhagen to fill those days.
This may not be your thing at all but if it was me I go see Thomas Dambo trolls! Odense or Svendborg as well as Copenhagen.