Were the priests keeping the money for themselves?

The chapter doesn't say. The priests were to take the money "each man from his donor; and they shall repair the damage to the house" (12:5), and "in the twenty-third year of King Jehoash the priests had not repaired the damage to the house" (12:6). The king asks, "Why aren’t you repairing the damage to the house?" (12:7), and no answer of theirs is given. The chapter says only that "The priests consented that they should take no more money from the people, and not repair the damage to the house" (12:8). It doesn't say where the money had gone. It does say that one kind of money was the priests’: "The money for the trespass offerings and the money for the sin offerings was not brought into the LORD’s house. It was the priests’" (12:16). It doesn't link that to the delay. Any reason for the delay goes beyond these verses.