I took it to the vet yesterday. (Originally was going to take the healthy one, too, but the healthy one was getting far too stressed out so I left him home. )
I brought the kaytee feed and a cut out sample of the newspaper on the bottom of their cage, with the concerning, red droppings. The vet took a small pinch of the kaytee feed, and wet it in a newspaper, and to my horror, the pinkish red seed bled red into the napkin. The red in their poops was likely from the kaytee feed dye. NOT blood. She confirmed this.(silly me)
Furthermore, she examined the dove, weighed him/her and also listened to their lungs. There was no respiratory illness, lungs sounded fine, no discharge or concerning signs around vent, ceres or anything. He/she was a little underweight though. The vet concluded that a new diet should be in order, and gave me an organic crumble-feed and I'm currently weaning them off of the kaytee feed and onto the new organic feed. I've observed both of them pecking up the feed today, so they are definitely eating! I'm glad.
I also have a small space heater see besides the cage to keep it warm for the, atleast until this cold weather passes. Speckleton, (the dove's new name) was VERY frazzled by the examination/trip. I felt bad when he started to whimper as she was feeling his crop/checking his mouth. But she was very well versed, and handled him slowly and gently. So I wasn't too concerned. Specklton and his companion Tim Pipppington, got a ton of quiet time after the visit, and both calmed down, good enough.
Thank you for your responses! I will keep you guys updated in this thread, on the condition of the two.

Crossing my fingers and hoping the diet change will be enough to turn them in a new direction.
-Nambroth; That's what I suspect, too, sadly. I returned the first dove thinking it was a fluke, and purchased the remaining dove in the store, to keep the first, healthy one companion. Little did I know that the new dove was sick also. My parents were urging me to take it back, since the bird was under a warranty. But I don't think I could return the bird, like some defect product. I already felt like trash returning the first. I'm really glad I stuck to my guns and took it to the vet, instead of just tossing it back to the store. I really hope the first is getting treatment, liek they promised. =/