Can I save this plant?

Hello Master Gardeners, I'd like to ask a question about this plant. Can it be saved, should it be tossed in the compost and the potting soil reused, or should it be thrown away (so it doesn't spread whatever illness it has). First Problem: I don't know the name of the plant, but it seems like it could be a string of watermelon. I would love to know what it actually is. I'll just refer to it as a string of watermelon. What Happened: I purchased some 2-inch succulents from a store last year. I brought them home and planted them in their own small pots. A small yellow threadlike vine came out of the string of pearls start and attached it to this string of watermelon plant. Where it touched, it curled tightly around the SOW. I removed the tiny vine with tweezers from the SOP and the SOW until there was nothing left on either plant. Oddly, the SOP went on to have a normal life with no blisters or visible spots and it has continued to grow and thrive. This plant has continued to grow, but each small droplet that has grown on the vine has gotten spots on them and has fallen off. It is still trying to lengthen its vine, but none of the droplets are spot free. Also, it is making a brave attempt to grow more shoots but I feel like I see another spot on a new droplet on the new growth. What to do? I would love to save this if it is possible. But I have no idea what to do. Also, I am willing to do a lot to save this plant, but I don't want it to spread to other plants (it doesn't seem to have spread but some of my other plants have other types of spots and I worry that it is possible. Thanks so much for your help!