That's a common problem. Breathing puts you into an unbalanced position, which is why it's so important to work on balance. I'm glad you continue to practice skate. How easy is skate? Do you know if you are under- or over-rotated in skate? Off your belly is enough rotation and that's harder to do than being flat or fully stacked on your side.
Another tip is to make sure your lead arm is not too deep when you breathe; in fact, it might work better if it's a little shallow. It provides balance here. If that arm is falling, you'll be lifting your head to breathe in some capacity which puts your mouth in the water. Keep your ear near your shallow lead arm and let your breath come from rolling to air... don't lift and initiate the breath before the hips help it happen. Hope this helps!