Did I get this FLEX situation right?

[Dholloway1962]

Team playing DP/Flex. DP is batting in 6th batting position. For some reason unknown, the Flex bats thinking she is the 10th batter. The 9 hole batter bats and creates the 2nd out. The Flex then bats and grounds out for 3rd out. Defense approaches before all left field and points out that Flex batted.

Here's what I did: Flex became an Illegal Substitute for the 1 hole batter by batting improperly. The 1 hole batter has now left the game and is re-entered by coach. The Flex is DQ'd for the game. The 3rd out stands. The correct batter when this team comes back to bat is the 2 hole batter.

Did I get everything covered?