My back yard was really torn up during hurricane Rita and giant trees were destroyed. Its now beautifully landscaped with Crape Myrtles, Irises, Agapanthus, Azaleas and Lilies. The flower bed is in full sun and has a sprinkler and the stupid Pennywort really loves it. It is growing in and under my new plants.

I don't mind it growing in the grass because we just mow over it and that slows it down a bit. I've tried mulching and now pull it out by the long horrible white roots but I know I haven't gotten them all. It keeps reappearing.

Does anyone know of another way to kill this pest? I really don't want to use poison because of pets and wild birds. This plant is like a monster and I hate it. Hopefully someone can give me good advise on how to kill it or slow it down. Thanks in advance.