As a native speaker, Dutch is the language I mix least of all (not that it never happens, mind you), but I understand your question very well. I had been learning German for two years, before I started learning Swedish, but from that point on it was as if all my German knowledge had flown out of the window. I struggled with the most basic sentences, somehow constantly mixing in Swedish words, or outright switching to Swedish - without noticing it - as soon as I didn't pay the utmost attention to what I said. I never really mixed much German into my Swedish, though - probably because German very quickly became the weaker of the two. After that one year of learning both, I went to university to study Swedish and didn't really speak any German for a couple of years. When I took up German again, I had to work fairly hard to keep both languages separate (and not simply forget my Swedish, like had happened to my German before). I don't know how common my experience is; there were several people studying both German and Swedish, an they seemed to be doing fine. Now I'm studying neither language, and forgetting both, but at least I don't mix them up anymore.
So yes, if I, as a native speaker of a Germanic language, can mix up Swedish and German, I see no reason why you couldn't mix up Dutch and a Scandinavian language. Don't take this as discouragement, it might require more work for some people, but that doesn't mean it can't be done.
Are you interested in learning Dutch?