מוֹרֶה is a participle-shaped noun (hiphil pattern) from the root ירה, and the standard lexica split it into two lexemes. מוֹרֶה I "teacher" belongs with ירה in the sense of instructing (hiphil הוֹרָה "to instruct, direct"), the root that also yields תּוֹרָה; the sense is secure at Job 36:22, Proverbs 5:13, and Isaiah 30:20 (twice). מוֹרֶה II "early rain" is treated as a byform of יוֹרֶה (Deuteronomy 11:14; Jeremiah 5:24), the noun deriving from ירה in the sense of pouring or watering; BDB and HALOT assign Joel 2:23 to it and list Psalm 84:7 Hebrew (84:6 English) there as well, BDB marking that verse doubtful, and DCH follows the same two-entry arrangement. Whether the two nouns rest on one root (casting or throwing, whence both the pouring of rain and the aiming of instruction) or on homonymous roots is not settled; the derivational discussion is carried in TDOT's treatment of תּוֹרָה.
The crux at Joel 2:23 turns on הַמּוֹרֶה לִצְדָקָה. The consonants admit "the early rain in right measure" or "for your vindication," and equally "a teacher of righteousness"; Jerome renders doctorem iustitiae, and the corresponding Hebrew phrase becomes a standing title in the Damascus Document (CD 6:11; cf. CD 1:11), which is why the verse figures in the history of the Qumran Teacher of Righteousness. The decisive internal argument for the meteorological reading is the second colon of the same verse, גֶּשֶׁם מוֹרֶה וּמַלְקוֹשׁ, where the word sits inside the fixed early-rain and late-rain pair; Wolff and Crenshaw both take the rain sense while registering the ancient teacher tradition. The same ambiguity recurs in the verbal form at Hosea 10:12 (וְיֹרֶה צֶדֶק), discussed by Macintosh, which is not an occurrence of this noun but shapes the argument around it.
Psalm 84:7 Hebrew (84:6 English) is the harder verse: גַּם־בְּרָכוֹת יַעְטֶה מוֹרֶה admits "the early rain also covers it with blessings" and, vocalizing בְּרֵכוֹת, "with pools," while the Septuagint (Psalm 83:7 in Greek numbering) and the Latin Psalter read the subject as a lawgiver (a participle of νομοθετέω; benedictionem dabit legislator). Kraus and Hossfeld with Zenger treat the line as both textually and semantically vexed. A neighboring vocalization crux stands at Psalm 9:21 Hebrew (9:20 English), where the consonants may be pointed מוֹרָא "terror" or מוֹרֶה "teacher, lawgiver." At Isaiah 30:20 the plural מוֹרֶיךָ governs a singular verb (יִכָּנֵף), and commentators divide between a reference to God, taken up in the standard English versions with a capitalized "Teacher," and a reference to the prophetic teachers restored to the people; Blenkinsopp lays out the alternatives. For the agricultural frame of the rain sense (the autumn yoreh from roughly late October, the spring malqosh in March and April, and their covenant weighting in Deuteronomy 11:14 and Jeremiah 5:24) see Borowski.