I think it sounds dreadful.. but thats my opinion.. based on RVing for years with my children.. in a 30 ft motorhome, comfy beds and our own bathroom. The public bathroom on the train ( which is invariably reported to be quite filthy by arrival in Rome) and the much much smaller shared space would drive me insane.
I suggest you try a shorter train journey with the kids.. 4- 5 hours first, then see if 13 hrs would be fun. There is no scenery to enjoy in the dark, the journey may be noisey or bumpy for light sleepers, and the worst part would be the train change ( with possibly tired grumpy tots and luggage ) .
I think my almost 6 hr journey on a very comfortable train cured me of thinking a longer journey would be fun. We had a nice trip , but found we were ready to get off by hour 5 ourselves. We had eaten our picnic( do not kid yourself, food on the train sucks, there is no nice dining car to go to anymore) , read our books, looked out the window( our daytime travel at least allowed that )
About 25 yrs ago I took some night trains.. cheap backpacking trip,, but since we could not afford a first class sleeper we considered them only a means to an end,, not a delightful part of our trip. I had hoped the "newer" trains would have transformed the experience for us.. but it didn't.
I would only do an overnighter now if it was on the Orient Express,, in a private cabin, with a private toilet. Maybe i am tired of roughing it..and I know I would be even less inclined with small kids.
I still take trains.. but 6 hours is my limit .