I am an a scientific artist and my work so far is quite seasonal. I am a non EU citizen (Australian). I am on a family re-unification visa and I pay Danish tax. Can I work in another EU country for the 'off season'/ Summer?
If you want to go for less than three months somewhere else in the Schengen area, you don't necessarily need a work visa or residence permit but, unless your wife moves to that other EU country with you, you do need some sort of authorisation to work.
Additionally, if you live in Denmark since more than 5 years, you might be considered a long-term EU resident and should be allowed to reside for more than three months elsewhere in the EU somewhat more easily. But you don't have an automatic right to work in another country – either short-term or long-term – and would still need to apply for a permit/authorisation as applicable.
So, these subtle distinctions aside, your status in Denmark does not fundamentally change your situation with respect to other EU countries. There is no easy solution for your problem, you need to get the local bureaucracy to issue some sort of permit before you can work in another country, even short-term.
On the other hand, if you are selling your services (not sure that's a phrase you would use of course!) under the guise of a company/as a self-employed person instead of seeking an employment contract, other rules might apply, I am not entirely sure.