Moses prayed for Aaron, but he also prayed for the forgiveness of the entire Children of Israel, both for this sin and for many others (for the golden calf in Exodus 32:11, for the sin of the spies in Numbers 14:13, for the rebellion of Korah in Numbers 16:22).
The verse in its context (Deuteronomy 9:18-20) is one of those cases in which Moses prayed for the entire nation of Israel, not just for his brother. After describing how he prayed for 40 days and 40 nights for the forgiveness of the sin of the golden calf, Moses says that he also prayed for Aaron, apart from his praying for all of the Children of Israel.
וָֽאֶתְנַפַּל֩ לִפְנֵ֨י יְהוָ֜ה כָּרִֽאשֹׁנָ֗ה אַרְבָּעִ֥ים יוֹם֙ וְאַרְבָּעִ֣ים לַ֔יְלָה לֶ֚חֶם לֹ֣א אָכַ֔לְתִּי וּמַ֖יִם לֹ֣א שָׁתִ֑יתִי עַ֤ל כָּל־חַטַּאתְכֶם֙ אֲשֶׁ֣ר חֲטָאתֶ֔ם לַֽעֲשׂ֥וֹת הָרַ֛ע בְּעֵינֵ֥י יְהוָ֖ה לְהַכְעִיסֽוֹ׃ כִּ֣י יָגֹ֗רְתִּי מִפְּנֵ֤י הָאַף֙ וְהַ֣חֵמָ֔ה אֲשֶׁ֨ר קָצַ֧ף יְהוָ֛ה עֲלֵיכֶ֖ם לְהַשְׁמִ֣יד אֶתְכֶ֑ם וַיִּשְׁמַ֤ע יְהוָה֙ אֵלַ֔י גַּ֖ם בַּפַּ֥עַם הַהִֽוא׃ וּֽבְאַהֲרֹ֗ן הִתְאַנַּ֧ף יְהוָ֛ה מְאֹ֖ד לְהַשְׁמִיד֑וֹ וָֽאֶתְפַּלֵּ֛ל גַּם־בְּעַ֥ד אַֽהֲרֹ֖ן בָּעֵ֥ת הַהִֽוא׃
I threw myself down before the LORD—eating no bread and drinking no water forty days and forty nights, as before—because of the great wrong you had committed, doing what displeased the LORD and vexing Him.
For I was in dread of the LORD’s fierce anger against you, which moved Him to wipe you out. And that time, too, the LORD gave heed to me.
Moreover, the LORD was angry enough with Aaron to have destroyed him; so I also interceded for Aaron at that time.
In fact, the incident of the golden calf is specifically held up as an instance of not showing nepotism, because the Levites didn't favor their relatives whom they were instructed to kill (Exodus 32:27, Deuteronomy 33:9 according to Rashi).
Making the golden calf was clearly an embarrassing sin, and Aaron's part in it is no exception, but for Moses to pray for his brother (as he does elsewhere for his sister, Numbers 12:13) is not a bad thing. On the contrary, "don't ignore your flesh" (Isaiah 58:7). Praying on behalf of yourself or your family is commendable.