Naples, 1 afternoon, 1 morning and 2 nights

With just 2 nights, this might work better.

Day
1. Explore Naples then train to Sorrento (2N)
2. Day trip to Positano by bus
3. Return to Naples via Pompeii

The Circumvesuviana is the local train that runs from Naples via Pompeii to Sorrento. Note that it is possible to store luggage at Pompeii.

Thanks, djp_sydney, do you mind also helping me with the concerns in regards to the location of accommodation in my post?

I have been a few trips in Naples and south. For 2 nights if u have no interest in Naples proper do not stay there. Opt for dreamy Sorrento but reserve soon. It is a big draw for tourists as it is stunningly beautiful. Easy boat rides or busses are avail to Amalfi, Positano. A day trip can be arranged for Pompeii by train etc. Naples is not for everyone as it is gritty altho there are many interesting and archaeological significant sights, museums if that is your interest.
With 2 kids I would opt for Sorrento, they could wander about more freely in Sorrento. NIghtly also is a fun paseo up and down "MAin St"! Families walk , chit chat and grab a gelato to go, oh so Italian! Your kid may enjoy the itailan stroll.

Thank you JS, my husband and I are adventurous, but I suppose safety is the most important thing when travelling with kids. We'll still visit Naples for its archaeology museum and the famous pizza, but will try to stay at Sorrento then.

For what you want to do, Sorrento is a better option.

Napoli Centrale is being refurbished, including the area around it, and is safe. There is a police station at the train station as well, next to baggage deposit.

I wouldn't skip Naples altogether on your trip (unless it's just too much and you've ran out of time). Just know what to expect...it's a bit gritty and very chaotic, but I would not worry about safety in the sense of getting mugged in the middle of the day (you do need to watch for speeding vehicles and vespas though, and keep good control over valuables). I traveled there by myself in my late 20s (solo petite woman) and had no safety issues, but it was a bit of sensory overload at first. As to your question about Holiday Inn that's too far away, I wouldn't do that in any city...it's better to be in the center and not rely on hourly shuttles.

Pompeii is huge and not easy to get around. I highly recommend Herculaneum especially with kids. It can been seen in 2-3 hours and you will see more preserved homes, rooms, colors etc. This also leaves room to do something else as travel time there is about 45 min from Naples if I recall correctly, went two years ago. You could see this site in the morning and go to the Naples archeological museum in the afternoon to see all the items taken from Herculaneum. I would not stay in Naples in the summertime, opt for Sorrento, it is only 1 hr to Herculaneum. Unless they are the last or first two and you have a long list of things to see in Naples itself.

David has given you great advice. Check your luggage at Napoli Centrale, hop on the metro to the archeological museum. Have one of Naples fabulous pizzas. Wander back to the train station thru the Centro Storico, pick up your luggage and hop the Circumvesuvian to Sorrento.
Sleep Sorrento.

The next day explore a portion of the Amalfi Coast either by ferry or bus. Eat plenty of gelato. Sleep Sorrento.

On to Pompei scavi via Circumvesuvian check your luggage at the site. Visit with guide, available at the gate. Your kids will get much more out of the area w/ guide.
Return to Naples and wherever else your travels will take you.

It's fast paced, but you'll have a great time. Sleep on the train.

Thank you gerri & live-from-New York, yes, we definitely will try to get a tour guide at Pompeii, thank you for reminding me. How much do they usually charge? At this stage, we will have to use Naples as home base as we weren't able to find suitable accommodation in Sorrento.

The price for a guided group tour of Pompei is 12-15E per person. Groups are 20-30

Thanks gerri