If 2/3 of the tickets sold were adult tickets, then 1/3 of the tickets sold were children's tickets.
The total number of children's tickets sold is 1/3 * 345 = <<345*1/3=115>>115 tickets.
If adult tickets cost $13.95 each, then children's tickets cost 23 * 13.95 = $320.85 each.
The total amount of money made from the sale of children's tickets is 115 * 320.85 = $36,918.75. Answer: \boxed{36,918.75}.