You're right that it comes down to preference. That said, I don't even see C as a reasonable option when compared to the other three. Why lose all that time just to get dinner in Stockholm and go to bed (by the time you get to the hotel and check in), for double your best cost option? Option B to BCN is only slightly better and I wonder how much of Barcelona you'd get to see.

To me, either A or D are the smartest options, to make the most of your time. For option D, the train ride would be 12-13 hours, correct? So you would only get a few hours to explore Venice with the kids. Would it be an option to fly VCE-FRA instead of take the train and gain an extra 8 hours in Venice on Saturday?

You also don't mention how long you'll be in Rome. Part of your consideration is whether you want an extra day there or not.