Rooting can take a long time. Some woman I work with has had little bits of the same plant on the windowsill here for weeks, and I can't see anything happening in the root department. Sometimes it's better to just start over.
My own experience with this plant is that it can't stand "wet feet" - i.e.,the roots can't stand being in wet soil. They rot easily if they stay wet. Good drainage is key.
You mentioned it's a hanging houseplant, but you say it has good drainage. Does it really? I mean, can excess water drip out the bottom of the pot, or does it drain from an inner pot into an outer pot? If the latter is the case, then it might not be good enough drainage. (Even though the excess water might drain out of the inner pot, it will be stuck in the outer pot, near the roots, where it will just create a yucky moist environment, perfect for root rot.)
I don't think the idea of watering it twice in a day is a good one. This plant prefers life on the drier side. Not cactus dry, but not 'living in a giant mud puddle' wet either. I aqgree with the poster who said to let the soil get somewhat dry between waterings. Again, not 'parched earth dry' - but wait until it looks dry-ish before giving it a drink.
Kiz- FYI - the Wandering Jew is not considered a noxious weed in the entire country (assuming you mean the US). I live in PA, and you can buy the plant in stores, propagate it, grow it outdoors, etc. Plants have different restrictions in deifferent parts of the country. Another popular plant here is Oxalis triangularis (the green ones are often sold under the name 'shamrock plant', but I like the purple ones better) - I understand this is a hated weed in California. But we actually buy it and plant it on purpose here - and there's no black market for plants - these plants are available in major stores.
So, yes, she's trying to get this plant to grow on purpose. It can be a very pretty plant, if you stop thinking of it as a weed.