whats your routing s/b no prob getting to Rome as UA,CO & US fly there but FCO is an AZ Hub = SkyTeam so no non-stops can be flown FCO-TLV = how are you flying FCO-TLV?
also who are you flying to FCO and whom from TLV back to the US?
Exactly- concentrate on getting to Rome with a US carrier and the same if you can on the return (even if it is only to cross the Atlantic) that will bring the taxes and fees down a bit.
from Rome to TLV you will have to use a non-US carrier with a stop in either IST, WAW, BRU, FRA, MUN, ZRH or VIE