Do clothes hanging on the line become impure after the impurity of a child's urine transfers to them through various stages, such as wiping the urine, pouring water, scattering droplets onto the clothes, and then the mother touching the laundry line with her wet clothes?

It appears you have many whisperings (waswas), and we advise you to disregard them and not pay attention to them, for that is the most beneficial cure for them. If the place of urine is washed in the described manner, it has become pure. If some water sprinkles from it onto clothes, it does not contaminate them. The mother of the boy passing over the place of urine does not contaminate her clothes. If these clothes touch the clothesline, neither it nor the clothes hung on it become contaminated. The default state of a child's feet is purity, unless there is certainty that they have been affected by urine. Assuming they were affected by it, and there is doubt about the transfer of impurity to the spot where the child moved, then that spot does not become impure, because doubt about the transfer of impurity has no effect.