From that of is not a phrase, as others have well explained. To make it yet easier for you or whomever to comprehend that sequence of words, here are some other word sequences that include that in like fashion.
- This spacecraft will give scientists the opportunity to compare the view from space with that from the ground.
- Your research study fails to relate performance on one day to that on any other day.
- Relate the governmental structure on pirate ships to that on merchant ships.
- The XAFS oscillation for all spectra shows a maximum amplitude in the
k range from 8 to 10, and that of C1 is identical with that of C2. However, that of D1 is two times larger than that of D2.
- Between the title of the strongest and that of the first occupier, there arose perpetual conflicts.
As can be seen, the pronoun that in such like sentences serves to avoid repetitive specification when one or more things represent the same sort of the thing that has already been specified in that sentence or in a previous sentence. That is so used most often for comparisons. But, as best seen in my last two examples, any relating of one thing to an already specified thing is fair game.
Lastly, for many people, this use of that sounds somewhat formal. At least in everyday parlance, they would rather omit that, if the grammar permits it for a particular sentence. (For my last one, it probably does - Between the title of the strongest and of the first occupier... -, though style might not, because ambiguity is maybe introduced, but I'm not sure.) If the grammar doesn't permit it (as in your sentence, in which no one would ever say differs from of hearing children), they'd rather either not avoid repetition or they'd phrase the whole sentence differently. For example: Emotional development of deaf children is different than of hearing children. Incidentally, Americans often say different than. Some people criticize it as incorrect, but that's unjustified, because that collocation is used by respected writers.