Q. A recipe for a marinade for chicken calls for coarse prepared mustard. Can I substitute spicy brown mustard?
Frankly, as far as mustard descriptions go, "coarse prepared" is so non-specific as to be almost useless. A prepared mustard is generally made from a mixture of mustard powder and water, vinegar, wine or other liquids, and various spices. A coarse mustard has had crushed or whole mustard seeds added to the mix. So a coarse prepared mustard could be just about any American-style yellow or brown mustard, a French Dijon-type mustard, a hot English mustard, any variety of German mustard, even a Chinese mustard, etc. as long as the seeds have been added.
Now, having mocked your recipe writer sufficiently, we want to give you permission to use any mustard you want. But, in that you are located in the US, we're guessing that your recipe writer has a coarse prepared yellow mustard in mind one made from the milder white mustard seed favored in this country, rather than the stronger brown seed. So a spicy brown mustard is probably not going to produce the flavor combination the recipe writer had in mind. It may still be delicious. You may love it. You may swoon over it. But it is probably not true to the recipe.
Do what you will.