Two questions, thoughts in general on visiting/going to the summit during Pompei day; and would you visit it or Pompei first in the morning?
I would never try to see Pompei and Vesuvius on the same day. When we have visited Pompei we have generally spent 6-8 hours there. That being said, if you must see both on the same day I would go to Pompei in the morning when it first opens and when it might be cooler and less crowded. Vesuvius tends to be cloudy in the morning and clear in the afternoon but it will likely be more crowded then.
We went up to Vesuvius first then took the short ride on the Circumvesuviana to Pompeii. It is a little demanding on the feet but if you don't have any health problems walking on cobblestones and up hill (to see the crater on Vesuvius).
You may get better advice if you say what month of the year, and from where you are taking the "Pompeii day." Any mobility limitations, sun or heat problems in the group?