House plant

When you come in our front door and look to the left you are greeted by this wonderful plant. When Mimi's friend Harriett was alive, she gave the plant to Mimi and Mimi kept it in her bathroom window. Oh green paw Kitty took the pitiful looking plant and gave it new dirt and found it's happy place in the house. I have to watch Maggie because if she gets too close that tail of hers can do some damage. I have placed it on the tallest plant stand I have but alas it is crawling along the floor again. I have cut it back only once and started some cuttings for Nephew who lives in Mobile. Some days I feel as if Nephew is part my child as his interests are the same as mine.  I may go in search of a taller plant stand as I cannot cut it off without rooting it and I do not know of anyone who I can give it. I take after Pa and Mother as they too could not just throw away a good cutting of a plant. Do any of yawl have this problem?
The Kitty Justice is I do not know the name of the plant so we refer to it as Harriett's Plant.