It may be wisteria vine?

It's difficult to hone in on the leaf shape. If you break a stem, does it exude a white sap?
I wonder if it could be Pedilanthus.

Here's your photo in the upright position.

Slipper Flower Pedilanthus sp.

Pedilanthus tithymaloides, AKA zig-zag, Jacob's ladder.
When outside in a warm climate it produces tiny red flowers that hummingbirds love!
The variegated species produces a pink flower, that the hummers think is 'so-so'.
Usually roots directly in soil, very easy. I just pruned and 'planted' some yesterday.

"They" are calling this Euphorbia now. Wash hands well if you come in contact with the sap/juices.

Do 'they' know how long it took me to remember the name Pedilanthus tithymaloides?

here is a more up close shot..

I have one of these, actually two, but different species. One is not quite so zig-zag. But when they get a little bit more sun than usual, they get a pretty pink hue to the leaves. It can be quite beautiful.

My variegated plants get the 'pink hue' to them
I have found that here is Costa Rica they produce more blooms if they are 'more or less' ignored and in the full sun, even in the dry season!

how can we root it? my mother has tried everything! she wants all the grandkids to have a piece of gramdma's plant...

Very easy to root. Just cut off a section lay it on an out
of the way spot for a day or two then pot up in a cactus
soil. It'll root within a week or maybe two if it's moist, not wet.

These are very hardy and incredibly easy to root. I pruned both of mine in spring and I have so many plants at this point that I just set them aside with other "to do" plants. Well, it turns out that they sat for almost 2 months! I am NOT kidding, I then stuck a rubberband around the whole bunch and just stuck them in my "junk" pot. My junk pot is a planter where I put plants that I don't have time to take care of because I need to mix mediums for them, clean and bleach a new pot, cut screen for the bottom, etc...Right now my junk pot has a Lipstick plant , a wax leaf red bloom Begonia, a small Kalanchoe and now a Pedilanthus or as I call it a Jacob's Ladder. I am astounded at the resilience of this plant. By the way, my original came from my friends Grandmother's tree, who gave it to her daughter and she in turn gave it to her son; my friend.

One more thing. The full tree that I got my original cuttings from had some hardening of the stems, which I was told is no big deal. Well, this year, all of the stems and pieces that had this hardening, died underneath. It looked like a dried up husk, it was awful! Luckily, the rest of the tree did not suffer the same fate. Is this normal?

Take cuttings from the newer tips of the existing plants and do what other posters advised.
If some parts have this 'hardening' remove them, and it won't take long to produce new shoot and fill in the spaces.

Thank you all so much for identifying this plant! my mother is thrilled! We are goint to try to root it and produce some more plants so we can all have some of grandma's favorite plant. i will let you know how we do!

thanks!!!!

I have rooted them in water , in a glass or vase.