Both are possible options. The direct Barcelona-Malaga AVEs are very convenient.

I would suggest as well the Barcelona-Malaga direct AVEs. You’ll save on reservation fees that way and also from Göteborg to Barcelona is more convenient than the route via Hendaye IMO.

It'll take a while to get there, but it is possible. There are multiple options and you'll likely pass through both of them. 

Depending on how much in a hurry you are or how tight your budget is, or what your preferences are in terms of transfers, there are a few options; it'll be a bit of a puzzle. 

You could try Göteborg-Frankfurt on day 1 (with changes in Copenhagen and Hamburg), the direct Frankfurt-Avignon TGV on day 2 and on day 3 the direct Avignon-Madrid AVE plus a Madrid-Málaga AVE. The Barcelona-Málaga AVE's are also good options. 

Both Madrid and Barcelona are nice and have much to see. If you have the time, why not visit both?