I haven't been to Port Lligat. I was surprised at how much I enjoyed the Dali Theatre-Museum in Figueres; I'm an art-lover but don't really care for surrealism. The DT-M is quirky enough that I think most people would enjoy it.
I recall an earlier post or two about hitting both the Dali sights on a single day-trip from Barcelona, so I know it's possible (if winter transportation schedules and opening hours aren't different), but it's not something I'd particularly want to do. Here's the way the transportation goes:
From Barcelona to Figueres you'd take the train. There are both fast (55 minutes, but usually more expensive) trains and slower (at least 1 hr. 41 min.) trains. They both depart from Barcelona Sants, but they use different stations in Figueres. The fast trains go to Figueres Vilafant; the slower trains to Figueres. Both stations are something of a walk from the Dali Theatre-Museum, but Figueres is a bit closer. (You can take a look on Google Maps to see their locations.) There's a local bus running between the two stations that has a stop a few blocks from the DT-M, but I don't know how often it runs on weekdays, Saturdays and Sundays. It was my impression the bus was scheduled to meet the trains at Figueres Vilafant, but I'm not positive about that. On the day of my trip, the fast train was 15 minutes or so behind schedule, and the bus had already departed, so I'd suggest being prepared either to walk to the DT-M or to budget for a taxi and research taxi telephone numbers prior to arrival in case there isn't a taxi waiting at the station.
From Figueres you'd need to take a bus to Cadaques, then walk 15-20 minutes to Port Lligat or take a taxi. The bus ride was very scenic in the summer. I don't know to what degree taxis are available at Cadaques. The latter is a very picturesque former fishing village, now touristy, with white-cube houses dripping with bougainvillea--though probably not in December. Cadaques might be fairly dead in December; I just don't know. Important: The buses to Cadaques depart from in front of the Figueres train station, not Figueres Vilafant.
My guess is that extending the day trip to Port Lligat would only be really worthwhile if your group has a strong interest in Dali or especially likes "house of" attractions (which I do not). However, I am only guessing since I haven't been there myself.
Both the Dali sights are quicker to reach from Girona, which is a very attractive historic city worth at least a full day by itself. I believe Girona is known for good restaurants, but it doesn't sound as if you have much extra time.
I should mention that I've seen references to one-day bus tours going to both Dali sights. I don't know that they run in the winter, and I think a combo tour would be a distant second choice since you'd be tied to the time the tour company allowed at each sight. A French bus tour showed up at the Dali Theatre-Museum while I was there. It left considerably before I did after spending about half as much time at the DT-M. I don't think any of the tour members went up to the second floor.
Furthermore, the ticket to the DT-M includes entry to the jewelry collection in a separate, nearby building. The collection is fabulous and shouldn't be skipped. If you don't try to take photos (nearly impossible to do successfully), it doesn't take long to see the jewelry collection. I was told one can go there before the entry time specified on your timed ticket for the DT-M itself.