where to stay between rome and amafi in april

Naples. Take your 7 year old out for original pizza in Naples.

I agree, Naples is very interesting and does have great pizza. We were there last March for a week. It is a gritty city, but we always felt safe and has no difficulty.

One night in Sorrento is another idea and depending on how you go can be on your way from Rome to Amalfi making that journey easier on that day and the following day. You can catch a bus easily from Sorrento which will take you directly to Amalfi.
Also has great views which are different than Amalfi and being a much larger town an overall different feel. Lemon trees everywhere and actually really good shopping if you like Leather and all types of clothing.
The shopping you will find in Amalfi is all tourist shops in comparison.

To reach Sorrento you can take a train or a bus from Rome. The bus is direct (kind of, makes little local stops in route) ; the train is not you will have to make a stop and train change in Naples but even with the stop the train is faster.

You could also try and work in a stop to Pompeii on that travel day from Rome.

I know Naples has some sites I would love to see and I do love pizza but overall the city is not my cup of tea for a vacation so I prefer to avoid it.

Or Salerno - nice little town with a medieval center and lovely sandy beach, access from Amalfi by ferry or bus, then fast train to Rome the next day.

I would recommend Sorrento. Easily accessible and not as hectic. We love Sorrento
Enjoy your trip.
Lorieann