"It's possible, but the reality is a lot of families split up when husband walked away to go to "America". It's very possible he came thinking he left the family because she refused to go and then she had a change of mind. Happened alot."
That would only make sense if the child that the wife arrived in the US with was older than 5 years. Otherwise, if the childless husband and wife "split up" in 1907 and he never returned to Italy, who is the father of the child that the wife arrives with 5 years later? It seems unlikely that the husband left for America thinking the marriage was "over" and so reported that he was single - but then 5 years later his wife and some child that couldn't have been his because it's only a year old and he hasn't seen his wife in 5 years show up and he accepts them both, raising a child that isn't his.
It was actually not uncommon during this period for Italians to travel back and forth to Italy, sometimes to find a wife. So this seems like the more likely scenario. My 2nd great grandfather made several trips back to Italy, each time returning to America single except for the last trip - his new wife followed him a few months later and I could confirm that they married in Italy because she stated on the passenger list that she had never been to America before. I know we think of the voyage to America as a once-in-a-lifetime trip but by this point in history it was not always like that anymore.
To the OP: I don't know if there are surviving records of arrivals in Italy - if there are, they are not on Ancestry.com. Likewise for outgoing US records. What I would look for now is their marriage record in Italy.
You should also look for the husband's second passenger list, returning to the US in what sounds like would have been 1911 or 1912.