Are a child's traits truly random?
You true randomness definition is partially wrong! Something does not need to be fundamentally random to be beyond known science.

Also, it is unclear what process you are referring to when talking about a child's trait. I would assume you are thinking about crossover but then, summarizing crossover positions by "child's trait" shows that you misunderstand a number of things! 

To my knowledge, outside of quantum physics, in no field of knowledge has it been shown that true randomness has any measurable effect. So, no what chromosome an individual inherits is only random in the sense that it would be necessary to know exactly the position of every molecule in the cell to know where the crossover will happen.