What appears is you have to convert the date to sql time stamp and then use to_timestamp method instead of to_date method to store the date with timestamp. Another point is if you use PreparedStatement instead of Statement it will be better.
First, use a PreparedStatement.
That will at least ensure that your SQL is not having escaping problems.
Next, what is the exact format of the two date strings?
Personally, I would convert them to java.util.Date and have the INSERT code somewhere else entirely, like a Data Access Object.
That way your SQL doesn't have to care at all about date formats.