What prevents Rabbi Yehuda from using the same verse for mulitple purposes, when Rabbi Yehoshua Ben Levi makes use of that verse to teach two concepts. "And you shall make known to your children etc..."
Yitzchak, Jerusalem, Israel
1) The Shitah Mekubetzes answers that the first way that Rebbi Yehoshua ben Levi uses the verse is in fact only an Asmachta. Rebbi Yehoshua ben Levi does not really maintain that a Ba'al Keri is forbidden mid'Oraisa to learn Torah. (See Bava Kama 82a, which tells us that Ezra instituted immersing in a Mikvah for a Ba'al Keri who wants to learn Torah. This shows us that mid'Oraisa a Ba'al Keri is allowed to learn Torah, as Ezra's enactment was a later ruling which possesses only Rabbinical authority.)
According to this, only the second way that the Gemara uses the verse, "And you shall make it known..." -- to teach that whoever teaches his son Torah is as if he received it on Mount Sinai -- is a genuine Torah Derashah. The first way the Gemara uses the Derashah -- that a Ba'al Keri may not learn Torah -- is merely a hint to the Din d'Rabanan; it is not teaching us a Din Torah. There is no dispute between Rebbi Yehudah and Rebbi Yehoshua ben Levi on this point.
(a) The Vilna Gaon, in Sefer Imrei Noam on Maseches Berachos, gives a different answer. To help us understand his answer, we should look first at Tosfos in Yevamos 4a, end of DH v'Ki, who writes that Rebbi Yehudah knew that it is clear that one can learn a new Halachah from every word in Mishneh Torah, or that every verse is "Mufneh"; that is, the verse is free and available to make a Derashah from it.
(b) The Imrei Noam writes in the name of the Vilna Gaon that since Rebbi Yehudah maintains that the verse, "And you shall make known...", is Mufneh, this means that after one has learned one thing from the verse, it is no longer Mufneh; the verse has already been used to teach something and cannot be used to teach something else. Rebbi Yehoshau ben Levi does not agree with Rebbi Yehudah. Rebbi Yehoshua maintains that it is possible to learn from a verse even if it is not Mufneh. Therefore, according to Rebbi Yehoshua one can learn several things from the same verse. Rebbi Yehudah maintains that if the verse is "Mufneh" only on one side, it follows that one may use the verse only once.