B'sha'ah tovah!
Yellow/brown discharge does not render you niddah. Even if the mucus plug is expelled and has reddish/pinkish streaks within it, it will not render you niddah, since that blood is not uterine.
In general, you need not consider yourself niddah in labor until you are having heavy contractions that make it difficult to walk unaided, or if you are fully (or mostly) dilated in the final stages of labor, or if you experience actual bleeding during labor.
Please see our article on childbirth for more details.
B’hatzlacha!