its good to be both man!
producing = problem solving
i think that's actually sound/mix engineering. Producing is more about the attitude and the ability to explain to the performer a way for them to get a type of performance out a particular artist, helps if they aren't understanding a concept or getting it just right.
But a producer can be a sound/mix engineer. They do have different problems to solve how ever...
Back on topic, i find that playing live shows or performing the music you make is a great way to stay motivated. But you shouldn't rely on that to continue making the music. You have to dig deeper to want to walk down the creative path, every thing else is icing.