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Most Kordes roses are not winter hardy in your zone. If you don't know which Kordes you have, go do Kordes-Rosen.com to figure it out. (It is a German website but the names are given in English.)Miniatures are often grown as indoor plants. I've attached a link to an article on growing roses indoors. https://garden.org/frogs/view/3508/
https://www.gardeningknowhow.com/ornamental/flowers/roses/planting-rose-bushes-in-the-fall.htm

Contact Winterthur to find out whether your rose is a grafted one or one grown on its own roots. (The info may be on their website.) If it is grafted, results of your cutting may not have the same vigor and winter hardiness as the parent plant. Fall is a good time to propagate from semi-hardwood cuttings, ones that still have some flexibility but not as pliable as new growth. Winter time is for hardwood cuttings. The attached articles discuss the 2 techniques.
https://www.gardeningknowhow.com/ornamental/flowers/roses/roses-from-cuttings.htm
https://www.rhs.org.uk/advice/profile?PID=387

It sounds like one of two things has happened. The rosebush has done what is called forming a Sport. A new rosebush put forth by the same rose. Or perhaps part of the grafting of the rose reverted to another portion of the graft such as having a burgundy and white iceberg rose. Or perhaps one color of rosebush grew in that location originally, someone thought it had died so planted another but did not get all of the root system from the first, thus you now have both growing up from what appears to be the same bush.

Having companion plantings with rosebushes can work but it is vitally important to keep well maintained food and water boundaries. It sounds like the ground cover plantings are stealing nutrients and water from the rosebushes feeder root systems. The ground cover needs to be removed back to a 16 to 18 inch diameter around each rosebush. They need that room for their feeder roots to be able to get the food/fertilizers and water without having to strongly compete for them. They are not getting enough nourishment to perform as desired. Ground covers survive on the very same nutrients and water that the roses need. Being ground covers they will win that battle every time. I recommend taking the ground cover out back to the diameters I previously mentioned. Then add some nice compost to the same areas working in to the soils lightly and then perhaps add a nice decorative mulch to help hold the ground cover plantings back. The rosebushes will thank you for it.

There is no need to destroy them just because of black spot. Spray them all with a fungicide called Mancozeb every 7 to 10 days for 3 to 4 sprayings. Once the black spots are on the foliage, they do not go away. However new foliage should be black spot free if the fungus has been killed. I have found mancozeb to be the best to stop black spot in its tracks! It will leave a yellowish powdery looking residue upon the foliage and canes but that is part of how it works. Once the new foliage comes in clean, keep the rosebushes sprayed with an earth friendly fungicide called Green Cure every 10 to 14 days unless wet conditions dictate more often. Mix it at the Cure Rate at all times for a higher degree of protection. Both products are available at Amazon.com.

It sounds like your shrub has rose rosette disease. Read the attached article and look up images on the web to confirm my suspicion. Clean any tool that you have used on it. https://www.gardeningknowhow.com/ornamental/flowers/roses/rose-rosette-disease.htm