First- this site is wonderful! I wish I had found it before today.
I have a desert rose I have had for about 5 years. I am by no means an expert but I have tried many different things to grow my roses and have found a few tricks over the years (including using all natural charcoal with NO soil and pine bark to plant them in). for whatever reasons, they grow like crazy. My rose is different then the type you can find at the big box stores. It has fuzzy leaves and a more interesting bark. My question is this. About 4 months back I noticed a sort of "shoot" growing from the side of the plant. It was never there before and I never "spliced" anything onto it. It looked like an out of place branch or something. Last week it produced a few buds. To my amazement, the flowers are not only shaped differently but they are a totally different color. I did some research to the best of my abilities and cannot find anything on this. Is this normal? Its a very beautifull and healthy plant but now it is "odd" with this strange 2nd rose growing out of it all the sudden. Can you tell if this is normal or do I have a "freak of nature" in my front yard?
OK, I am a bit confused about the Roses you have, the Desert Rose known to me is actually a form of Cactus, then you mention your other Roses, are these other Roses the same as in Desert Roses, or are you talking about Rose bushes climbers or shrubs, I cant help you for Desert Roses as I grow these in my greenhouse due to our climate here in UK, I would imagine the new shoot your noticing is a new bud / stem that has came from under ground/ soil level, IF it is maturing to look the same as the parent plant then you would be best to just allow the plant to grow on as normal, maybe when the new has matures a bit more and there MAY be roots appearing from it, if this is the case, cut the new shoot away with a sharp knife and after the cut part has dries out a bit, insert it in the same soil mix as the parent plant.
Someone else may come in to give you better advice than I can, but I personally would do the same with my own plants.