Question: How long must a child wait between eating meat and milk?
Answer: He does not have to wait at all because he is a child. We obviously have to educate him, but if there is a need, he does not have to wait. Sometimes we serve a child meat and he eats with difficulty, and soon thereafter he is hungry. Or, we want him to eat more and we give him something else, like Milchigs. Some Rabbis have established guidelines that at a certain age a child should wait one hour, then two hours, then three, etc… (See, for example, Shut Be'er Moshe 8:36), but this is not definitively set from a halachic perspective. It is certainly logical that a child should slowly be educated so that he will be able to wait the required amount of time by his Bar Mitzvah. In Shut Yabia Omer (Volume 1 Yoreh Deah #4), Ha-Rav Ovadiah Yosef discusses this issue and writes that it is a case of a double doubt: The first doubt is that perhaps the Halachah follows the opinion of the Rishonim, such as the Rashba (Yevamot 114 and Shut Ha-Rashba vol. 1 #92), that it is permissible to give a child something to eat which is forbidden by the Rabbis (although in practice we do not hold this way – see Shulchan Aruch Orach Chaim 343:1) and waiting between meat and milk is a Rabbinic prohibition. The second doubt is that perhaps the Halachah follows the Tosafot (Chullin 105a) that there is no obligation to wait between eating meat and milk. It is forbidden to mix them, but if I eat meat, clean the table, wash my hands and brush my teeth, it is permissible to eat milk (although we do not hold this way in practice either – see Shulchan Aruch Yoreh Deah 89:1). Therefore, there is no problem with giving a child under Bar Mitzvah milk after meat when there is a pressing need.