Good morning Mattias,
I'm sorry to hear that you've run into this too. I've found that there's one heck of a learning curve when it comes to secured print services...
Initially, I published a secured service from ArcMap with embedded credentials, but that inexplicably broke a few weeks ago. I then revisited the idea of publishing via Pro (much preferred) and since our Portal deployment uses web-tier authentication for secured items the new service generally works without the need for any additional scripting/embedding of credentials--if one of my Enterprise users is already logged in, based on their Windows credentials, then they can easily print secured items.
Which method are you using to publish from Pro? I recall looking at this documentation for help, in particular the first paragraph. Depending on how your Portal is secured, on your application server you may need to change the setting in IIS that disallows web-tier authentication for the ArcGIS Server web adaptor only.