I think it's an ordinary Kalanchoe blossfeldiana - it needs a bigger, proper pot with drainage holes, and cutting back to about 1-2 inches all over. Your grandmother might remember it as a small plant bought in flower originally, perhaps. It's grown like this because it does not have enough root room and is unable to put out new stems and be the bushy plant it's meant to be. After cutting back and repotting, find a sunny spot for it if possible, although mine flowered again left standing on a windowsill in bright daylight with very little sun indoors.
This link https://www.plantsrescue.com/kalanchoe-blossfeldiana/ suggests cutting back and moving outdoors during the warm months of summer, but as I say, mine flowered again with just keeping it indoors. My own plant has become rather leggy (probably needs more sun) and now its finished flowering, I am about to cut it back hard to encourage more bushiness.