I am taking care of this plant for my mother who has gone back to Florida for the winter. The only thing she can remember about it is being told it is full sun (it's one of several plants in an arrangement that spent the summer outside at a camp). I brought it indoors October 15th and it bloomed with in 8 hrs, but the house got cold over night and it dropped it's flowers. We got the heat up again and steady between 65 and 70 and it's been blooming every morning and closing every night for about a week. It is however dropping leaves like crazy and I would love to know what it is so I can stabilize it for the winter. I'm guessing it's a sedum from the look of the vines and leaves, but I can't find anything with flowers like this. I could be completely off. Any help is greatly appreciated!

It looks like Portulaca umbraticola to me:

Thank you so much!