"I stubbornly" is correct and usable in written English.
You can use it when you want to emphasize the strength and determination with which you are performing an action or expressing an opinion. For example: "I stubbornly refused to believe her excuses."
Because I stubbornly refuse to observe Opposite Day".
I stubbornly did not step off the bike once when ascending any lung-busting hill.
Although I stubbornly refused to praise her unexpected decorating, I left every piece where she put it.
But I stubbornly suspect that only the cultist, or the academic, is capable of swallowing an author whole.
It could easily have been rewritten in a different way, but I stubbornly wished to check it.
It was past sunset, and they told me to stay the night there in that village, but I stubbornly decided to come home over the mountain.
It is rather like World War I, when stubbornly obsolescent generals wasted millions of lives throwing infantry against impregnable in-depth defenses.
I'm ready to face those challenges and I'll stubbornly embrace the best for myself, my future, my family and all whom I can help".
I was baffled by this conceptual-leaning gag at the time, but as I've learned more about contemporary art, I remain stubbornly excited about art's capacity to throw me--albeit figuratively--across the room, to pull me into a warm embrace, to send my mind deep into thought, or to set my nerves on edge.
At the office, where I'd established a long habit of friendliness, I stayed stubbornly at my desk, staring at my screen and limiting myself to the briefest of exchanges, which themselves were not difficult to replace with gestures — a nod, a wave, a smile, a shrug.
What I have though is a plan, a five-year plan to turn around the party, and I'm stubbornly sticking to it".
