Since your wife and the second child are having similar symptoms, the rash seems to be contagious and such a rash which spreads so fast is most likely due to viral infections, fungal infection, bacterial infection or scabies. It will be best to get the sore cultures for bacterial, viral and fungal infections and then specific treatment can be started. Diagnosis of scabies is made by scraping the skin and viewing the material under a microscope to see the characteristic mite or eggs.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.