The phrase "impossibility of determining" is correct and is commonly used in written English.
It is typically used to refer to something that cannot be determined or measured accurately, for instance: "Due to the huge range of variables involved, there is an impossibility of determining the exact cost of the project."
You did a good job in stating the impossibility of determining cause-effect issues in your child's case.
Acknowledging the impossibility of determining a market bottom "until we look back six months after the statistics have come out," Ms. Kelley said she is blunt about that point with prospective buyers.
See Note, 6 Hofstra L.Rev., supra n. 7, at 563 (harmless error "is inaccurate as a test for ascertaining the prejudice resulting from misjoinder because of the impossibility of determining the extent of that prejudice").
A provision of this sort is needed because of the unequal bargaining position of authors, resulting in part from the impossibility of determining a work's value until it has been exploited.
Polls predicting primary-election results get the outcome wrong because of low turnout, the near impossibility of determining accurately who will and will not vote, and the extreme volatility that sometimes occurs after interviews have been completed.
Much of our delay in understanding what category or phase to assign to swine flu has stemmed from the near impossibility of determining just how many Mexicans were infected with the H1N1 virus, a figure that now appears to have been far larger than initially guessed.
But a limitation that we can expect in the future experiments is the difficulty (or even impossibility) of automatically determining the equivalent mutants.
Extensive discussion is given over to the impossibility of experimentally determining a "metrical" simultaneity relation that is, of finding experimentally a unique simultaneity 3-space for an inertially moving observer.
Streat argues compellingly that the issue of irreversibility is a practical impossibility to determine, and that because of this, utilitarian criteria should prevail in determining when death is pronounced and when organs may be retrieved.
The absence of an economic approach to the system implies the impossibility to determine the optimal size of the system, to locate the most urgent sites to give priority for installing the radar devices, and to analyze its financial sustainability.
The beauty of this reasoning is that it spares the judge the headache of determining who is right on the tax point, probably an impossibility for a judge.
