The stain probably is acidic, if your unsure test with ph papers. Cat sick has so many nasties- stomach acid food colourings ets. What has probably damaged the carpet is the solutions she has allready put on it, vanish and similar products contain bleaches which can affect the colour of the carpet and help to lock the stain in.
If you still want to have a go, try rinsing with plain hot water then use a neutral spotter. You might want to add some de-foam to the tank, you will spend 15 mins just getting the vanish out.
I would leave it at that. You could try an emzyme digester followed by ammonia then acid rince, but this could make the stain worse thus becoming your problem.
Mark.