Italy in April or July?

How heat tolerant are you?
July will be hot.

I've been in April and March. Weather was very comfortable both times--shirt and fleece or windbreaker jacket. If I had the choice, spring.

Venice would be such fun for the kids! Try Row Venice, which offers small group rowing lessons on the quiet back canals, about 100 euros total for ninety minutes for your whole family. The kids can see who picks up the techniques the fastest , as it's harder than it looks!
If Possible, avoid Italy the week before and the week after Easter- the crowds are really bad when all of Europe is also on holiday.
In July, you have heat and humidity and crowds- I would avoid July .
If you choose Venice and Rome, fly into Venice, out of Rome. Early morning flights out of Venice can be a challenge. Have a great family trip!

July is as hot as hell on fire, in Rome especially, but also Florence or Venice.

April has generally a much milder and pleasant weather, but in terms of crowds, it is also very busy. There is Easter week, then Easter Monday, a major holiday, then the 25th of April (Liberation Day holiday), then May 1st, Labor Day all over Europe. Most European school trips with hundreds of school groups take place in April.

So choose your poison.

My family spent a month in Italy in July (on my 2nd trip) and never again. We've spent four months in Italy in March/April, including Easter weekends and Easter Mondays. We've taken our kids and grandkids to Italy 3 times --- everybody's favorite place for a week was Venice, then a few days in Rome (especially going to Ostia Antica and Castel Sant'Angelo). We did take the kids out of school a couple days early on the theory that travel was far more educational, also because they would be jet-lagged. Highly recommend flying into Venice and out of Rome.

There are plenty of posts and trip reports about taking kids to Italy --- here's mine from taking our grandkids to Venice & Rome & a couple other places in December: https://community.ricksteves.com/travel-forum/trip-reports/bologna-ferrara-venice-rome-in-december-with-kids

If you are thinking about going this year and you decide on April start making hotel reservations ASAP. Pickings were already slim in early December when I planned my April 12-28, though you may not be as budget-conscious as I am. And then look at booking some attractions and experiences. I've looked into several high interest sights in Rome and Venice and see that they are filling up.

In July and August, every Italian that can avoids the city like the plague due to heat. It is really not the time for sightseeing. If you were to go to Italy to hang out at the beach for your stay, that’s very bearable - but outdoor sightseeing is quite possibly a nightmare, with temperature highs of 100-110. You might be able to plan around it a bit by staying indoors 11am-4pm, but have to bear that in mind.
Easter is in early April, so depending on what mid April means you might be able to avoid it.

I have been to Italy in July, April, May and September.
Since I am from a hot place in the USA (South Georgia), I am used to the heat in July in Italy. You may not be?

April, May and September is nice.

Suggest Rome and Florence. The High Speed trains only take about an hour and a half between the cities.

When we traveled in Europe, I always had my teens read books about the. history of where we were visiting.
One thing, if you go in April, avoid Rome during Easter.