London to Southampton cruise port

You haven't indicated where your starting point is -- presumably you're leaving from a hotel in central London? Personally I'd want to get to Southampton several hours before the cruise departure, because you never know about delays with transport. Is Windsor Castle a true "must see" for you and there's absolutely no other day on your trip when you can fit it in? Or have you chosen Windsor Castle because, as the crow flies, it looks like it's on the way? In the latter case, my advice is to just find something else to do near your hotel in London that morning. After you check out, asking your hotel to stow your luggage for a couple of hours, then come back & pick up your luggage and take a train that will get you to Southampton by, say, 2 PM.

Check this advice about trains from London to the Southampton cruise ship terminals. https://www.londontoolkit.com/travel/southampton_train.htm

Windsor is quite a detour by public transport between London and Southampton (one word). Personally, I would pick somewhere in London to visit that is within easy reach of Waterloo station.

What is the best way to get from Windsor to Southampton? I will do the first tour at 9:45 and see the changing of the guards. I can arrive at the cruise ship by 3pm. Another option is to spend the night before in Windsor and leave my luggage at the hotel during my visit. I'm limited on time and this is my second trip to London.

I think you are complicating your life, but it is your life to complicate. Why not save Windsor for another time and just get to Southampton with lots of time to check in on board your ship and then maybe do a quick tour of S'hampton? If your ship is leaving at 4:30 then 3:00 is not when boarding starts, it is when boarding is just about closing.

"What is the best way to get from Windsor to Southampton?"
Option 1.--Take a short bus ride from Windsor to Heathrow Airport, Terminal 5, then purchase a ticket at the bus station (T5) window for Southampton coach station. You will exit through the glass sliding doors, and sit on one of the benches to wait for your bus. Be sure that your bus isn't already sitting there. When you arrive in Southampton, the bus stops at the coach station--not the cruise terminal. So you will need a taxi for the short distance from the coach station to your cruise terminal.

Option 2.--Contact one of the well regarded limo services, such as "Just Airports" and get a price from them as to what they would charge to pick you up at Windsor and deliver you to your cruise terminal. It's not going to be cheap, but you'll get there.

Option 3.--Take the train back to London. Get to Waterloo Station; take train to Southampton; takes approx. an hour and a half to two hours.

Do read the London Toolkit page that epltd gave you in his link. It has some good information for you.
Here is another London Toolkit page with information about Southampton.
https://www.londontoolkit.com/travel/southampton_national_express.htm

"Another option is to spend the night before in Windsor and leave my luggage at the hotel during my visit."
It's a good idea to spend the night in Windsor if you are determined to visit Windsor this trip.

What about the previous afternoon? Is there any possibility you could leave London at lunchtime the day before, train to Windsor, drop bags at hotel, see Windsor that afternoon? Spend the night in Windsor; then leave the next morning for Southampton.

It is also a good idea to do as Norma suggested, and save Windsor for another visit.

You may want to get a quote from this service:
http://www.chauffeurtravel.co.uk/blog/luxury-transport-to-cunard-southampton-docks
Contact James O'Neill at Chauffeur Travel and get a quote. Tel. number is 44 1225 463 404 from outside UK or go to www.chauffeurtravel.co.uk. Email is [email protected].