Dipping oneās hands in a river: [1]
Dipping oneās hands three times into a river is questionable whether it removes the impurity.[2] Thus, one is to re-wash his hands properly pouring three times from a vessel.
[1] Kama 4:12; MāA 4:10; Mamar Mordechai 4:7; Chayeh Adam 2:1; 159:22 regarding washing hands for bread; See previous Halacha and footnotes there for the background and explanations of this ruling.
[2] Although dipping three times into a river is similar to dipping oneās hands into three different vessels, nevertheless it is possible that the impurity only becomes removed from the hands through pouring from a vessel. [Kama ibid]