when a dog drinks from a vessel of water and a cat also just touches the water which is not just a little bit and after that touches me. is my clothing now impure and does a washing mashine suffice?

If the cat was wet with the water the dog drank from and touched your clothes while still wet, that spot is washed seven times, one of them with soil, and a washing machine counts if it rinses and spins it seven times. If you are not certain the wetness reached you, your clothes stay pure.