I live in Riverside, California (about 60 miles east of Los Angeles).

My garden is loaded with Senecio vulgaris (common groundsel) and
Euphorbia peplus (petty spurge).

When hand-weeding, what's the best way to make sure I pull ALL of the
weeds ("ROOTS AND ALL").
'
grab them at the base and pull gently until the root lets go, if the
stem breaks you are pulling too fast. Practice will tell you how much
pressure to use with each plant and your soil.

For heavy soil and plants with taproots, such as Oxalis corniculata, you
can loosen the soil with a three pronged hand mattock before trying to
pull them. Avoid turning the soil, you will expose more weed seeds.

After weeding, what can I apply to prevent these weeds from re-
emerging? (Preen Weed Preventer doesn't work)

Try other kinds of pre-emergent read the label for kinds of plants that
are controlled or use mulch
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09=IX