Flight from US to Rome then Venice

Immigration in Rome as that is your entry to Schengen
Customs in Venice

4 hours should be plenty of time as long as arrival is on time

Is this all one ticket or same airline?

You will have to work out your transportation into Venice proper, seems like train would have been quicker/ cheaper/ easier

Where did you check train schedules?

It will be two separate flights the first one from the US to Rome and then I booked a flight on ITA from Rome to Venice. Since it’s our first time to Italy we have no idea on times as far as immigration, how long that will take So we decided Staying at the airport and taking a flight to Venice would be the easiest less stress way to go. We need to be in Venice on the day we land in Rome. Our flight from the US to Rome is a nonstop.

As I remember you should be able to stay behind security. Just follow the signage. But you may have to change terminals.

Here are your options for getting from VCE into Venice
Scroll down to Aussie’s post
https://community.ricksteves.com/travel-forum/italy/getting-to-venice-from-airport

You should be able to get in to Venice by 8 pm or so
Customs is just a matter of walking thru correct door-no real time involved

Immigration at FCO can take less than an hour
Depends how many flights arrive at that time

FCO website has info on transferring, maps etc

As noted, as long as your incoming flight arrives on time, you should be OK. As to staying airside, it depends. What airline is your Venice flight on? I see that this is on a separate ticket. Does your carry on luggage meet the requirements (both size and weight) of that airline? Does that airline allow you to check in and obtain boarding passes online? If yes, then you can stay airside. If not, you need to go outside the secure zone to check in, then go through security to get to your next gate. Check in and baggage requirements will be on the airline's website.

If you fly United to Rome, United and ITA Airways are both partners in the Star Alliance, so you should be able to check in your luggage all the way through VCE. If you are flying with Delta or American they might still be able to check your luggage through VCE, but you need to ask at the check in desk in the US. If they do make sure your bag tag says both FCO and VCE.

The airline in the US (except for maybe United) will not be able to give you the FCO-VCE boarding pass in the US, so even if they are able to check your luggage through VCE you will need to get your ITA boarding pass in Rome. There are several ITA transfer desks at FCO, on the airside of the terminals, try with them first, so you don’t have to exit the security gates.

Between Trenitalia and Italotreno there are direct high speed trains to downtown Venice every 40 minutes. I don't get why having no idea about "immigration in Italy" should led you to waste time flying to Venice airport (that's 30 minutes away from the city center).

Too much hassle for a 1st day of vacation, I'd rather sleep on a train while Florence and Bologna can be seen from the window.

I would rather take a train as well but OP has already booked this flight.

OP
Is the flight to Venice refundable?
If so and if you are interested in taking train instead-let us know and we can help you with that

Do you have to fly into Rome? Rather than, say, fly from the US into Amsterdam on Delta and then on to Venice on KLM?