Tradescantia fluminensis - Wandering Jew

How can I rid my garden of this weed, I,ve tried pulling it out,
spraying with "round-up" etc, and all that did was kill everything
else, heavy frosts don't affect it, boiling water , haven't tried
Costic Soda, or Battery Acid.

The big trouble is, it grows under tthe valuable plant's

Anyone got a simply easy, no-come-back way of getting rid of it.