As a retired painter and I also had the same difference of opinion with my DH -PAINT the shed-otherwise it will drive you crazier then a crooked picture. As a rule out buildings should match the house. Covering that awful red won't be as bad as some would think. The paint stores will tint the primer to make it easier. I prefer Zinnsver but Kilz is also a good product. Take a sample of the yellow with you and they will know how much to tint it - Prime the whole trim and all covering yellow with white paint is so much easier -Go see SherwinWilliams