Dear FRIEND,
I do not about law , but I Think she is doing right , because if she mentioned half day for your late coming , then this amount is too much more then as compare to you overtime amount .
eg: if you have 20 minute late and this will happen in 6 times in a months ,it means your total half day is 6 in a month or 3 leaves in a month or 240 hours . and according to your words she will deduct only 120 hours . and dear sorry i m also not aware from law , but after your discussion i am also study on this topic .