Answer: The mimosa tree is botanically called Albizia julibrissin. In my experience it does not do well in a container for very long, partly because it has a tap root that is ill suited to container growing and partly because it needs very intense sun during a long growing season to stay healthy.
There is another plant, Mimosa pudica, that can be grown as a houseplant. Sometimes it is called sensitive plant. It can be started from seed and it looks a lot like a baby mimosa tree. I think this is probably what that woman had. I hope this helps.
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