train travel

Milan to Venice, then to Rome and Florence and back to Milan works.
You might end up subtracting as you plan. (Milan is the one that I would subtract but you are flying to and from there).

You should buy these direct routes requiring seat reservation in advance for best prices

Milan to Venice
Venice, to Rome
Rome to Florence
Florence to Milan
These are the sites to use (compare)
https://www.italiarail.com/
http://www.trenitalia.com/

The daytrips are on Regionale Trains no seat reservations and the prices don't change so you can buy them when you get there from a machine as long as you have a card with a chip.

Here is a one stop site primer on taking the trains in Italy that may be duplicated in the responses
https://www.seat61.com/Italy-trains.htm

To Add:
For rail between larger cities I'd take a look at Italo as well as Trenitalia, and personally wouldn't use Italiarail.

http://www.italotreno.it/en

The fast Frecciarossa and InterCIty trains require reservations and tend become more expensive the closer you get to departure, because the cheaper seats sell out. So the sooner you can set your travel dates in stone between cities, the more money you'll save buying the train tickets now. You can buy them all on the Trenitalia website and print them out if you like. If you aren't sure of your schedule yet, you can wait until later or even until you get there and book at the (probably) higher fares still available in August.

Most trains you'll be taking between those cities will probably be the Frecciarossa and IC trains. Regional trains as noted above don't have reservations are are the same price day of departure as they are early - you don't have to buy those in advance. Take note though that if you buy regional train tickets from the machines, you MUST validate them in the ticket machines at the train stations, BEFORE you get on the train! If you get inspected and are found not to have a validated ticket, you WILL be fined - no warnings are given to naive tourists. Any ticket you buy that has a reserved seat for a specific time and date does NOT need to be validated, though.

But Italy's train system is terrific in general - a great way to get from city to city.

Going Milan-Venice-Rome-Florence-Milan or any combination of those cities makes sense to me.

"no warnings are given to naive tourists..."

You mean no breaks are given to travelers who buy tickets and do not read and follow the rules.

"no warnings are given to naive tourists."

While the rules are clearly stated and usually enforced, I've seen both extremes. Some ticket agents are ruthless and will collect every last Euro, and NO amount of pleading, begging or whining will change that. I've also seen the other side where kindly ticket agents will simply make the tourist pay for the reservation or whatever they should have had, with no fines levied. The *best** policy is to learn the rules and follow them!*

Any roughly circular route of travel is fine. If you have hotels booked and are ready to reserve some of the longer, faster train rides, then that can be cheaper than paying full fare on short notice. Kids qualify for discounts in either case - see the details for Bimbi Gratis and Offerta Familia, one of which must be purchased at least two days before traveling. Age qualifications vary.

*Some ticket agents are ruthless and will collect every last Euro, and
NO amount of pleading, begging or whining will change that.*

the above perspective sounds like someone of means (on the receiving in) with a sense of entitlement .

But of course all with the means to travel thousands of miles
lets be aware to learn in advance to follow the rules wherever we go

Full disclosure in 2002 I got a 50 euro fine at Roma Termini (in the metro on the way to Vatican city when the station was not automated as today) for not validating my ticket.

"the above perspective sounds like someone of means (on the receiving in) with a sense of entitlement ."

Perhaps I'm misreading the intent, but that statement comes across as somewhat "misinformed", to put it politely. For the record, I'm not "someone of means" nor do I have a "sense of entitlement". I was simply providing my observations from many train trips in Italy.

Thank you I am overwhelmed trying to figure out destinations that won't break the bank but we can still enjoy for us and the kids. I was even thinking of stopping in Bologna. We want to see as much as possible but I know sometimes less is more

It can be overwhelming at first but once you start playing with the Trenitalia website you will get the hang of it!
Tips:
1) Use the English version of the website (button on upper right)
2) Know the names of your train station in each city, For instance Rome AKA ROMA has over 10 stations, You want to use Roma Termini. Same with Florence you want Firenze S.M Novella etc. Also make sure the start time for your search is "0:00" so it will pull up all of the solutions for the day.
3) You do not need to register for the site, continue as a guest and your tickets will be an attachment to an email that you print and present when asked.
4) You will be asked to pick a coach and your seats. You can pick four seats together all facing each other and there will be a table between you that is great for eating lunch. If you have a long train ride you can buy lunch before you board and eat during your journey
5) We purchased 1st class for not much more than 2nd class because we purchased 90 days before our trip and we felt it was a better ride and a value for the price we paid, but up to you. Make sure you have access to a sweater or jacket as it can get chilly with the air conditioning.
6) Once you get to the train station your "Bin" (track) will be posted about 15 min before your train leaves. You could be looking at a monitor located at Bin 2 and your Bin could be 24, you then hustle, with your luggage, to your Bin along with all the people on that train (imagine open seating at a Rolling Stones concert) you then walk down the bin to find your coach # and they are marked above on an electronic board and you hustle to that space and wham that train in there and everyone has about 10-15 min to get on. It can be a rush and this is why is it so important to do carry on only.

Once you buy your fast train tickets and are familiar with the site, when you go to the machines to buy your regional tickets you will be able to navigate as the machines are the same as the website. You will be fine!