By my 6th trip abroad, I feel like I finally have a hang of recovering from jet lag. My first trip abroad was to England for work back in 2014 and I did not do well while there (so I felt like a rubbish employee) and the return to the states was equally as bad. I feel like it took a week to get back to myself.
This trip to Italy though was much better. When we arrived in Italy, after having slept most of the 7 hour flight over, we just kept ourselves moving until a reasonable hour of 8/9 PM to sleep. Then our first full day we had a structured 12 hour bus tour which kept us engaged, but allowed for a pisolino (nap) on the bus before our last stop. After that we were good for the rest of the trip. I remember catching a nap one day, but do what your body says it needs. My body said get the hell off your feet.
On the return to the states, we got out for a nice walk before heading to the airport since the flight was 9 hours. We each napped once on the flight toward the end. I will admit, we did have the complication of our plane not being able to connect to a gate for an hour and being detained for a bit because we had a unknown to be forbidden small salami in my bag, but when we made it home we slept well until our typical waking hour.
I napped once the day after travel and felt really good after a shower. Since then I have just been sleeping like normal. Going to bed at 10 PM and getting up at 6 AM. I did use melatonin supplements when I felt I might need them. I feel like if I take it an hour before bed, I get more restful sleep. I just needed to listen to what my body was telling me. It has just been SO much better this time.