What do I do with 2 bird species laying eggs in the same nest?

Recently, we have had a pair of Cardinals lay eggs in a nest on one side of our yard. They abandoned that nest, and there's a new one on the opposite side of our yard. I'm not sure if these are the same Cardinals or not, though. We just discovered this new nest today, and the intriguing part is that there are 3 Cardinal eggs in the nest, as well as what appear to be 3 Mourning Dove eggs. We've seen the Cardinals flying back and forth from the nest, but we haven't seen the doves. I don't know if we should leave all 6 eggs there, or if we should move one of the species to the abandoned nest, or if we should "adopt" one species, and hatch and raise the babies. Please help if anyone has ANY idea what to do, because I haven't the slightest idea! Thanks!