Is two weeks enough time to drive from Tallinn to Stockholm and have enough time to visit the major cities along the way?

The trip is approximately 2900 km. So it is on average 207 km per day. That is not too much for a roadtrip with a lot of relaxing. And to do even more relaxing you can spend some days at the same location and then travel for half a day until you stay some days in the next city.

I did a lot of roadtrips in Europe and all of them were very relaxing even so we drove 10'000 km in 30 days. (three times).

The good thing is: If you notice that you can't relax you just travel slower and stay longer at the same place. Then at the end of the trip you have one very long trip, but that isn't really a problem immo.

Your itinerary would look something like this:

Overnight ferry, Stockholm to Talinn. Day 1 Talinn Day 2 It's about one day's drive to Gdansk. You might instead, want to stop at Riga (half day's drive). Kaunas is a bit out of the way. Day 3 Riga. Day 4, Half day's drive to Gdansk. Day 5 Gdansk. Day 6 Drive to Rostock. Day 7, Rostock. Day 8, Drive to Copenhagen. Day 9, Copenhagen. Day 10 Cross to Sweden (stop in Gothenberg?) Day 11, Gotenberg. Day 12, Head north. Day 13, Stop. Day 14, Finish trip to Stockholm.

A bit late, but partly based on my own experience: I’ve done Gda?sk – Vilnius – R?ga – Tallinn – R?ga – Klaip?da, single driver, albeit I did the trip in summer. From Gda?sk onwards is an educated guess based on map data.

There’s an overnight ferry from Stockholm to Tallinn vie Mariehamn. An itinerary would look like this:

1. Tallinn
2. Tallinn – R?ga (about 4 hours)
3. R?ga
4. R?ga – Kaunas (about 4–5 hours)
5. Kaunas
6. Kaunas – Gda?sk (about 8 hours)
7. Gda?sk
8. Gda?sk – Rostock (about 7–8 hours)
9. Rostock
10. Rostock – København (via ferry Rostock – Gedser, about 3 hours driving, 1 hour on the ferry plus 1 hour for check-in)
11. København
12. København – Stockholm (via Øresund bridge, about 7–8 hours)

If you squeeze this into two weeks, including the two surrounding weekends, and depart from Stockholm Friday evening, you can add up to four extra days to your itinerary. You could, for instance, add a day in Helsinki or one in Vilnius (which is about an hour from Kaunas and, since there’s a motorway from Panev?žys to Vilnius, takes about the same time from R?ga). Or, once you are in Gda?sk, you could consider Gdynia and Sopot as well.

From my own experience, Gda?sk–Kaunas was the most stressful part of the trip. Most of it is along DK16, which goes through villages and is quite narrow, with a bunch of trucks, which cuts down on your average speed. (Do note that I did this leg in 2011 and, as far as I remember, there was no expressway from Elbl?g to Ostróda then). Plan plenty of time for that. The same might be true for the Gda?sk–Rostock leg.