Herein is my battle (me vs oxalis) story for the past 12 months.
Problem - Rid the Dymondia of Oxalis without killing or replanting the Dymondia. In addition to Oxalis, there were two other weeds in abundance (but not nearly as abundant as Oxalis) in my Dymondia: spotted spurge which is common in California; and another weed that I have not yet identified(it is vinelike and sends up tiny thin shoots straight up about 2-3 inches above the Dymondia).
Severity - The Oxalis was rapidly taking over the Dymondia as of June 2010. In some areas there were spots as large as 5 inches in diameter where the oxalis had squeezed out the dymondia almost entirely.
Hand Weeding - Hand weeding was very time consuming and entirely unsuccessful with both the oxalis and the spurge as it came back much faster than the Dymondia could infill - and it even seemed to come back better! The oxalis root system is very extensive under the Dymondia in a lateral direction and the roots will break (in the soil I was dealing with which has some clay in it) prior to being able to pull out any significant amounts of oxalis. Maybe if the soil was a silty loam hand pulling would be an effective means of control - but certainly not in the soil that I was dealing with.
Triclopyr - Got some ortho weed be gone for chickweed, clover, and oxalis. I found that the best way to apply this (after trying brushes, q-tips, sponges between calipers) was by first putting on thin latex exam gloves (to minimize skin absorption) then putting thin cotton gloves, then dipping fingertips into the triclopyr and touching the oxalis. The oxalis grows very close to the Dymondia so it was hard to get the oxalis covered without getting some on the Dymondia. I erred on using very little triclopyr as I did not want to kill the Dymondia. I did this a few times during the summer of 2010 but the it was not very successful. It seemed to stress the oxalis but I likely did not apply enough to successfully kill it. In one spot I spilled a thimble of triclopyr and after a few weeks the Dymondia was very stressed and close to dead in that area. Prior posts stated that oxalis was very waxy and that a surfactant would be needed. I tried it both with/without surfactant and found it was nearly impossible to coat the oxalis without it and difficult to coat even with it. I am not saying that the triclopyr would not kill the oxalis, rather, I am saying that the methods I used were not effective and that getting the proper methods (application, strength, etc) that MAY have worked would have involved more trial and error than my resources would permit.
Pre-Emergence Herbicide - After doing some research I found only one that was listed for use on Dymondia for control of oxalis - Pendimethalin. Other pre-emergence herbicides that I looked at may have been safe but they were not listed as such. The product purchased (at Horizon which is big in western states) was Pendulum 2G - a granular product that comes in 40 pound bags (for about $100) - which covers a huge area (I imagine that you can also get it at John Deere Landscapes and Ewing if they are near you). I applied a dose in early january 2011 and another dose about 8 weeks later - not sure that my application timing was perfect - but that is what I did.
Winter 2011 Weather - I live about 25 miles inland from San Francisco where we have much hotter summers (over 90 on most summer days) and colder winters (we get a few surface frosts each winter that 'freeze' leaves but does not penetrate the soil). This winter we had some cold nights (mid 20s) and a couple of especially heavy surface frosts.
June 2011 Status - Presently there is practically no oxalis and no spurge in the Dymondia. This is a HUGE change since fall of 2010 when the oxalis clearly was poised for winning the battle come summer 2011. I am GUESSING that the winter frost 'killed' off the existing oxalis as it was thriving in January and gone in the spring. Further, the Dymondia not only filled in all the bare patches formally occupied by the oxalis but is also more robust and thicker than ever. The vinelike weed has been hand pulled this spring and has not re-emerged.
Conclusion - I am GUESSING that the success in ridding the Dymondia of oxalis is some combination of ; 1) winter frost; 2) vigorous infill/growth of the Dymondia; and 3) use of the Pendulum 2G - with how much, if any, of the success being attributal to each factor unknown. This is about the 3rd winter for this Dymondia and other winters did not seem to kill off the oxalis (or if was killed it came right back in same locations from seed so it never seemed to be gone). Some of the above is conjecture - but clearly the oxalis was killed and prevented from re-emergence - so you may want to consider the above if you have a similar issue to deal with.
Hope this helps!