This is unfortunate and probably the judgements you made, as an inexperienced traveller, were flawed. The key lessons people travelling internationally should learn are:
1. Always allow significant time for transfers, not just the minimum the airline allows. In this case, I would typically seek to arrive at least 3 hours at Logan before your Alitalia flight goes. Airline delays are common, and should be planned for. When booking, you can reject a connection time if it is too short and ask for a longer transfer time.
2. It is rare for airlines to "hold" an aircraft when there are delays. Holding an aircraft can cause the airline to lose a "slot" and can introduce very significant delays. Equally, if Alitalia hold the flight for you in Logan, those who are transferring to other flights in Rome may have missed their connnection.
3. I think you now realise it was a mistake not to accept the offer of the AA flight the next day. By the time you decided to try and "catch up" the window of opportunity for a transfer had passed. It is a shame that someone did not warn you of the consequences of this decision, but I am afraid you made a poor judgement based on inexperience.
4. Once a bag is in the system, it can be hard to retrieve, particularly if there is an interline, international transfer. You would have been well advised to proceed to your destination and allow the airline to try and get the bag to you. As it turns out, the predictable outcome was that the bag ended up in Rome where you could have retrieved it. (It is not illegal for a bag to travel without a passenger, otherwise how could the bag have got back to the US? Bags travel all the time without their passengers. The rules relating to bag matching are complicated, but it is the airlines responsibility to get the bag back to you).
5. Catching up with your party once you got to Rome may have seemed scary to you, but in fact public transport in Italy is good and you had nothing to fear.
It is a shame... and I can understand how upset you are. You have indeed lost so much more than money. Italy is an amazing country and you have lost a fantastic lifetime experience. That is very sad, but if this initial delay was weather, I am afraid I don't think you have a substantial complaint against either US Airways or Alitalia. Let's hope others can learn from your mistakes to prevent it happening to anyone else in the future.
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