Most likely there is nothing wrong with your transmission.
No, it doesn't seem to like to go into 2nd gear ...... especially while it is relatively new and never likes to when it is cold.
Like mentioned, work on your shifting technique.
Yep, some folks have found that a change in transmission oil helps.
In time, your transmission will get broke in .....and you will "learn" how it likes to be shifted....
PS - I don't reckon the short shifter is helping the situation .....
humfrz