What works best to control "creeping charlie" weed?
Creeping Charlie is very difficult to control. It is best to try to control it chemically.
The product I've had the best results with is 'Trimec', that's the trade name for an active ingredient. Many companies produce products containing trimec, Ortho, Gordon's and Bonide all do for sure. I prefer the Gordon or Bonide products, though that's strictly personal preference.
Go to your local independent garden center and look for their selective herbicides (weed killers). Find the strongest % of Trimec on the active ingredients list. Choose that product. Again, Bonide and Gordon's each make a version for difficult to control weeds (Ortho may, I'm not sure). Follow the directions on the product.
It will take a couple years to beat it back into submission. It sounds like alot of work, but it's not that bad. I'd do it.
By-the-by, only pull it as a last resort. Any roots you leave in the soil, will regenerate into more creeping charlie. You'll have a 'hydra' like situation, where every head you cut off becomes two more!
Good luck-
I hope that this helps