Family with babies travelling through frecciargento

Smaller suitcases (carry on size and maybe midsize) can be stored on the luggage hold overhead above your seat. Large suitcases go in a luggage hold at the ends of each train car. You may not be able to keep an eye on these from the seat, therefore I suggest you tie them together with a cable lock, just in case.
I'm not a fan of traveling with so much luggage, especially on the trains, since you have to take them aboard, but it's up to you. If you can lower your load, I suggest you do so.
You will have enough time to alight the train in Bologna. The train stops less than 5 min. but that's enough. Make sure you are near the exit with your luggage ready to get off, when the train pulls into Bologna Centrale station.

Your question makes me a little nervous as it reminds me of a train experience.
4 of us adults were traveling with our baby on the train from Venice to Salzburg.
We had a short time to change trains. We got stuck behind some very slow moving
passengers disembarking with a lot of bags, packages, luggage etc.
Panicking, we handed our son out the window to our friends on the platform. They had
managed to squeeze out ahead of us.

We also had a lot of luggage, bags and our baby's stroller.
We barely made it to our other train.

Whatever you decide, have a great trip!

Is there enough time to hold and get out all the luggage and baby stroller before departure of the train from Bologna?

This isn't a real problem if you can remember the estimated time of arrival in Bologna.

You are supposed to be near the doors before the train stops at the station, but conductors stay on the platform and of course they don't give the green light to the engineers if they see there is still somebody getting on or off. Would you do it? https://www.youtube.com/watch?v=OWogQlebNuA Watch the 2 conductors at the minute 9:16 through 9:37 .

Passengers can prevent train doors from closing and trains can't leave with an open door.

One adult stays on the platform with the kids, while the other hands all the stuff, thousands do it every day. The real problem is travelling with so many things to carry around: once out of Bologna airport, you'll have to load all these things on the bus to the city and this is just the beginning.
Keep in mind that Bologna station is underground, but there are 74 kms of tunnels before it.

The real problem is travelling with so many things to carry around:
once out of Bologna airport, you'll have to load all these things on
the bus to the city and this is just the beginning.

That's my concern as well. I don't know where else you are traveling in Italy (or in Europe) but you very well could be fighting those bags in many, many situations. With only two adults - and one of them managing 2 babies and a stroller - how are you going to manage 6 large bags? Travel in Italy (and some other counties) involves having to deal with steps and cramped spaces. It's not at all unusual for hotels not to have lifts, and to find lifts out of service or no lifts at all at smaller train stations. Trying to cram them all onto public transit would be a problem as well. The best thing you could do is to halve that amount of luggage and plan to do laundry as needed.

Those 6 bags would also likely cost you a fortune to check on a domestic Rome-to-Bologna flight.

Thanks for all reviewers , actually I am going for 1 year not for a short period of time or tourism.
My concern also is there enough space to store all this during the journey?

Ah, I see. So you only have to get from Rome to Bologna, which is your final destination. Then Roberto and darioalb have offered up some good suggestions. Best of luck, and safe journey!

For one year, can you ship items ahead or leave packages for friends to forward to you at your final destination ? Or pare down what you bring and plan to buy additional clothes as needed? (Small children will outgrow a lot over a year.)

As best I can tell, you would have 3 minutes to get off the train in Bologna. The 2 Freccia Argentos that do not require a train change between FCO and Bologna arrive there at 7 minutes past the hour and leave for the next stop at 10 after. The same 3 minute gap seems to be true if you take a Freccia Rossa. By myself with only a small carry-on and tote, I'm not sure I could get off that fast. I didn't check regional train schedules.

You might need to look at other options using Rome2rio. If it were me moving, I'd fly and let someone else manage the luggage to my final destination, even with the long layover in Rome. That is what you mean by "transit"? If that's not what you mean, Alitalia has flights from FCO to BLQ that last about an hour and leave at 10:20, 14:50 and 21:15.

The train is not going to leave while people are still getting themselves and luggage off, no matter what the schedule says.

The train is not going to leave while people are still getting themselves and luggage off, no matter what the schedule says.

Thanks Lola :)
The video I posted shows exactly the way conductors check if there is some people getting on/off and only after they give the green light.

I can't understand why some scare other travellers saying that you have only 3 minutes. In summer trains are often late because there's a lot more people travelling with luggage and they can't leave in such a short time. Of course you must get up, pick up all your stuff and wait by the door before the train stops, if not even 10 minutes wouldn't be enough.

Secondly I have alternative way which is connecting flight Home-Rome-Bologna?

From this statement, it looks like you will be arriving that day at Rome Fiumicino Airport that day. So I assume you are planning on taking the direct Frecciargento from the airport to Bologna that leaves at 11:08. There are only 2 of these every day, the other one is at 15:08. Keep in mind that if your flight experiences a substantial delay and you can't make that train, you will need to take a train into Rome and connect to another of the very frequent Freccia type trains to Bologna.

Better each adult and older child take their own airline regulation size rolling carryon bag. If you add (say) a RS Euro Flight Bag each, which you may also take onboard, you have many places to tuck in some baby items needed just to make the trip.

Keep weight of bags under the max airline rules and comfortable enough for each person to manage the bag with ease. E.g., I keep my rolling carryon bag at max 15 lbs. Somebody on this Forum travels with a carryon at 11 lbs., I wish! My RS Euro Flight Bag contains my travel laptop and iPhone, and a few purse items like a tiny throat spray, a row of Hall's, a small Tylenol, and a small travel packet of wet wipes.

Even nice 1st class train cars may have long, steep, narrow stairs up and down, wide enough to accommodate only half a foot. The older children may have to manage your bags too along with their own as you get the babies up and down. So keep everything light! You'll have to buy stuff after you land anyway, I know I always do, ship it home or leave items with hotel staff.

If you are ever connecting trains, and you have tickets needing validation at boxes in the station, I learned the hard way to validate all those tickets before you get on the first train. Often, trains are late and there's No time to validate subsequent legs of the trip. But you have to validate those tickets, if needed, before you board the connecting train.

I'd leave purses at home, wear a neck wallet and/or money belt. Rick Steves Travel Store online has some nice items.

Better each adult and older child take their own airline regulation
size rolling carryon bag.

The OP said in a later post that they're moving to Europe for a year, and not for tourism so it's understandable that they're going to have considerably more luggage than the usual tourist.