I’m sorry for your situation, but it clearly that you can only use in your home country the Interrail Pass on two days (Inbound/Outbound Rule). 

A possibility, would have been to use day trains from Nord Sweden to Stockholm and then with the Nighttrain to Malmö, or when possible directly change on the Snälltåget Nighttrain to Hamburg/Berlin.

In the first case you would have to pay a normal ticket from Malmö to the first station in Denmark to not use a second day in your home country. (If you enter a train before Midnight CET, you use only one day. If you enter after midnight CET a new train with the pass, you use a new one).

In the second case, your pass is ok. 

For the journey back, the best way is with day trains to Stockholm and from there nighttrains to nord Sweden, so you use only 1 day in your home country. Or using Snälltåget Nighttrain from Berlin/Hamburg and “change” in the app the train in Denmark so you stay in the train, but change it in the app to get only one day in sweden.

In your case I would get in touch asap with customer service via email or Social Media: 

customerservice@interrail.eu or on social media @Interrail 

and also check your case or make a new one here: Submit a request – Eurail Knowledge Base

Actually it is not really unclear. It is clear that interrail is basically not valid in your country of residence! there is just this two days on which you can use it anyways. but they only implemented this improvement a few years ago. the rule is simple. when you need an travelday, and you do a part on your residence countries tariff area, you also need an in/outbound day. (or separate tickets for the homecountry part)

The rules are clear, you can board trains on 2 travel days 00.00-23 59 (CET) in your home country. So you will need to buy ordinary tickets from Copenhagen and to your home in Sweden. 

If you live very long from the border and need more than 24 h to get abroad there is a special rule that you can use if you have a paper pass. This rule doesn't work with the mobile pass though. 

@Claudi.Moll  Can you look at this please.

Thank you for flagging @AnnaB ! We try to make the in/outbound rules as clear as possible, but I understand that there remains a lot of room for confusion. Essentially each Interrailer is allocated one outbound journey to leave their home country and one inbound journey so that they can return. As with all other travel days, in/outbound days last from midnight to midnight and during that day you can take as many trains necessary to exit/re-enter your country of residence. 

We do appreciate that this is not always possible. Travel days might be affected by strikes and delays which makes it impossible to complete this journey in one day. This might also not be possible for instance for travelers who need to travel from/to remote locations. In cases like these, we recommend that travelers reach out to customer service either by email or social media so that we can provide further assistance. Customer service is swamped right now but we do try our best to help asap :) 

@Claudi.Moll 

They apparently did reach out to Customer Support 2,5 weeks ago.

@AnnaB I'm following up on this as we speak, thanks! I really hope that we get a hold of the backlog soon 

Dear Claudia Moll,

is there any information we can provide which will help you to find our case?

Best Regards

I've just sent you a personal message requesting more details. I'll take care of this for you personally as soon as you've responded :)