Local Trains from Italy to Switzerland vs Bernina Express

"If we want to leave early in the morning and return at night, which train is better?"
Answer: whichever train leaves at the time you want to travel. As you say, the named "Bernina Express" and the local trains travel on the same tracks and you see the same mountains out of the window.
The local trains (like all rail lines in Switzerland) run once per hour. So, to leave early and retturn late you would need the local trains.
The only difference is that with the hourly local trains you need to change trains. With the named "Bernina Express" it is the same train all the way from Tirano to Chur.

You can look up train times here: https://www.sbb.ch/en/
The first train of the day leaves Tirano 07:41, arrive Chur 12:04
The last train giving a connection through to Tirano leaves Chur 14:58, arrive Tirano 19:00

Children 6 to 16 travel at half price on all Swiss trains.

Regular trains are not really "a fraction of the cost" of Bernina Express trains, you just avoid the mandatory reservation fee. Otherwise the transport cost is the same. Also, you will have to change trains along the way. The children can travel on a Child Day Pass for 16 CHF while adults pay the full fare. For a same-day return ticket, that would be 126 CHF per adult. You can see the kids will get a substantial discount.

I'll guess that you want to see the scenery you will pass, and that will have to be in the daylight.

The end of December is the time of the shortest day. Depending on exactly which date and exactly where you are on the journey it will vary slightly, but if you were on flat ground to the horizon sunrise will be a few minutes after 8. Sunset will be a few minutes after 16.30 - 4:30 pm.

The problem is those beautiful mountains. They give buckets of shade, and the track winds around a great deal so much of what you see will be in quite a lot of shade - if there is anything like a clear sky - for the first hour or two at each end of the day.

The first train back from Chur doesn't leave until 12:58 and it returns to Tirano at 17:00 (5pm) so at least the last hour will be in darkness or nearly so.

Do not buy separate tickets. Instead, buy a Saver Day Pass on SBB website (www.sbb.ch/en) that allows unlimited one-day travel on the Swiss Rail Network (except for a couple mountain railways which are nowhere near the Bernina route).

With maximum advance purchase, these Saver Day Passes cost as little as CHF 52 per person, then price increases in batches until the full price of CHF 150 (or something like that) for non-discount spot purchase on the day of travel (so it is a Day Pass, not a Saver Day Pass any longer).

The passes are only sold online.

The Engadin area is very beautiful. You could take a morning train from Tirano, spend one afternoon/night in Davos or St. Moritz, and come back the next day.

Thank you all for your advice. Bernina Express one way from Chur to Tirano it is. We have also decided to buy the Swiss Travel Passes. It covers the Bernina Express trio (minus the reservation fee) and also travel to the other Swiss towns we want to visit. Thank you for all the help.