You only have nine nights on the ground assuming you meant that you depart on the 19th --- arriving on the 20th - and departing on the 30th. This is classic example where an open jaw ticket -- into Venice and home from Rome -- would have saved time and money. (Advice is for other readers). Since part of the 24th and all of the 25th will be dead time you barely have enough for the original plan of Venice, Florence and Rome without adding Naples. Remember, when you change locations you lose at least a half day if not most of the day checking in and out of hotels, travel, etc. So your nine nights shrink in a hurry.
You might consider the 20, 21, in Venice, 22(travel),23, 24 in Florence, 25(travel), 26,27,28 in Rome, 29(travel) Milan and home on the 30th. Train schedules will be limited on the 25th but that maybe the best use of that dead day. Not an ideal situation but you can make it work. Just understand the limitations.