Do you wear padded cycling shorts inside trousers while daily commute?

No.

I just use a comfortable thicker-heavier padded mountain saddle. (NOT A LARGE OVERSIZED COMFORT SEAT. seat covers slide around too bothersome) usually type of seat found on cheaper end bikes.

Never used a BROOKS SADDLE. but heard once broken in ITS COMFORTABLE. but can take some time to get molded to bike operated by SINGLE rider.

____

clothes = just regular everyday clothes, on casual and active side. (almost anything which can be found at a sporting goods store) then outerwear (rain gear, winter...) 

Hiking cargo pants, lightweight poly-cotton t-shirt... 

I carefully rolled my pants and carried them in a back pack. I used padded cycling shorts when commuting. I commuted 17 miles each way, year 'round for many years.

Try riding to work with cycling shorts and with regular clothes and decide which is more comfortable and how much trouble that comfort is worth. Is the comfort of bike shorts worth the trouble of changing into trousers when you arrive? 

https://youtu.be/f4I3hQ8zeUE

No.  And never met anyone who has done this.  Sounds like a dumb idea.  For short trips, under 10 miles or so, you don't need padded shorts with a Brooks Leather saddle.  

https://youtu.be/iQmvlq5BMMA

I have never done that, it sounds awfully uncomfortable.