I don't mind driving here, but of course I am used to it.
It seems like this is another situation where there probably is no wrong decision; price, personal comfort, and, flexibility can all play a role, and the drive is not particularly difficult. You come through Lübeck so you could potentially drive there, spay the one night, then come on to Hamburg, though I would say that if you stay in Lübeck and only do a day trip or two to Hamburg, you do Hamburg more than a disservice.
For Schwerin, you can do it as a full day, but you could also combine it with Wismar if you are particularly ambitious. But I wouldn't. I would say it is a relaxing day to see a beautiful old town and a stunning castle and grounds. And if you want to see a bit more, stop along the Schaalsee (Pauls Hofküche in Zarrentin is good), which is at the edge of a UNESCO biosphere. You'll have seen a lot (also just on the drive there!) and not felt rushed.
For Hamburg, first things first: You will want a reservation at Miniatur Wunderland--book that ASAP. The dates of your trip are already tight. Getting the first thing in the morning tickets is the best option. It's less crowded for the start of your visit.
Brunch in the Coffee Roastery is a great option. It's a bit pricey, but the food is great and the coffee amazing! And it isn't insanely expensive.
Then walk across the bridges through the Speicherstadt to the Traditionsschiffhafen Sandtorkai. Enjoy the small pier with unusual ships and be sure to check out the brick work--the fish in the wall opposite the Sandtorkai, the tops of the houses along the Speicherstadt--the brickwork is really what makes the Speicherstadt special. From there, you're pretty much at the Elphi. Grab a ticket, go up to the viewing platform, and see Hamburg from above. Then grab the ferry #72 to Landungsbrücken, the landing bridges. The far end of the Landungsbrücken (LB) is the starting point for the Maritime Circle Line harbor tour. This tour is German and English, and it will take you into the harbor pas the big container ships (complete with explanation), to the Ballinnstadt museum, (I would skip this unless you have a family interest or tons of time--it's great, but not an absolute must), the Maritime museum (again, I would skip it--I absolutely loved it, but your time is too short), and back to LB. It is a hop-on, hop-off, so that is an option if you have other thoughts. Back at LB, you are pretty much at the Alter Elbtunnel, so go down and look at the tunnel, taking the car elevator back up. It's a quick thing and you'll be glad you bothered.
From here I have two recommendations, and of course it will depend on how you are feeling. The first and probably what I would recommend is to continue along the waterfront past the UBoat Musuem (Soviet post WWII submarine--fun, quick, but probably too much) to the Fischmarkt. This takes you past Park Fiction (on the other side of the road you are following) and its hippie / leftist culture. Überquell Brewery there is a great place for a beer and a meal or just a beer. You could also continue and eat at the square at the Fischmarkt if you haven't eaten already. Or if you are up for walking just a bit further (a few hundred meters), you end up at the Altonaer Fischmarkt, where you can eat at a number of great seafood places. We love Rive for its Jewels of the Sea seafood platter for two, but I can also recommend Henssler Henssler, am kai, and Fischereihafen. All four are Michelin listed ("good cooking"), but there are also other great seafood places in that area, including Asian fusion.
My other option in the next post.