Okay - I have resolved the situation. I appreciate the explanation above. It truly helps to know whom I am dealing with.

First of all, I want to thank you both for your advice. It was quite insightful, and I appreciate you taking the time to help me.

(1) I called back AA and the agent (who seemed helpful stated that she could book 4 seats together on MXP-JFK for about $600 and 4 seats together on JFK-LAX together for $650. The AA agent stated that she would recommend going early to the airport on the day of the flight, as there would be no way that they would have a 2- and 4-year-old not sit near a parent.

(2) I call back Connexions/“Chase Rewards” who gave suggestions of seats to AA together but restated that these seats are ‘not guaranteed’ and she strongly recommended for me to go to the airport early

(3) I decided to check the AA site again, and - somehow - it now allowed me to change seats/pay for seats. This configuration was not an option to me hours prior to this, and I wonder if the AA agent adventantly or inadvertently ‘opened up’ the seat map for me. I was able to get 4 seats together/middle 4 for MXP-JFK, and I paid about $250 to get 3 seats together adjacent to another aisle seat for JFK-LAX. How exactly did the seat map open up when there were no options to even pay more for seats prior to this? This I don’t truly have an answer for ...