The slightest bit of research would have quickly answered all your questions.

If I remember,this OP has a few days in Rome.Of which this "day trip"is taking one...
Exactly, Lucapal. As near as we were able to figure out, the OP has only 2 full days in Rome + late afternoon/evening of another. Along with the fact that doing both Pompeii and Vesuvius from Rome in one day would be exhausting, using up one of only two full days for that is seriously shorting Rome.
Also, I remember that the teenage daughter is a budding artist/has an interest in art? While there's certainly extant decoration in Pompeii (although as already mentioned, a lot of it has been moved to the museum in Naples) there's a larger amount/wider variety of art in Rome. Just IMHO.
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