How to properly clean carpet from Najasah?

I have a nephew younger than two-year-old and a grandfather older than seventy five. It sometimes happens that they can't hold their bladder and dirty the carpet. It is not easy to roll the carpet each time and send to carpet cleaner. I can't wash the carpet as easy as my clothes because of its bulky body. Then how can I properly clean the carpet from the Najasah? Is wiping with a sponge using detergent enough to make it Tahir? What if some water drops from the sponge to the carpet when I am cleaning the carpet? Do I have to clean the carpet from unseen dirt(dried urine) ?