The most simple solution to a miss match between a Drum kit and playback with any VST drummer is... Do not trigger the VST while recording drums.
Monitor the drum kit Brain and focus on a good performance.
Hi Hats can be multi samples and are integrated into the foot pedal positions of the kit.
Pre sets in some VST's like AD2 have a whole range of notes assigned just to the hi hats.
Once your happy with the performance you can easily edit the midi data to match the VST kit.
Make sure snap to grid is on when you drag the notes up or down.
You can move all the notes of any value but selecting them using the left side bar keyboard GUI. Clicking the note on the GUI will highlight all the notes of that value. Now simply drag up or down to the note value that matches the correct sound.
Session Drummer for the most part is GM compatible so pretty simple to use. You might want to read the manual for your drum kit to see if it can be set to GM mode, My Yamaha kit can be mapped.