1. "While El Al will fly that route nonstop starting in November, there are currently no nonstops available, so they flew British Airways with a connection in London and returned with Iberia Airlines with a connection in Madrid."
= You are switching tenses within the same sentence. It would sound more concise to write something along the lines of: "They flew B.A. with a connection in London...since El Al is only starting their nonstop route in November."
2. "This, despite the fact that they were on a single ticket on a single airline from Miami to Tel Aviv via Madrid."
= Incomplete sentence. You can just make it one sentence that reads: "When they asked for the Iberia boarding passes for their connecting flight from Madrid to Tel Aviv, they were told that they would need to request new boarding passes after landing in Madrid, despite the fact that they were on a single ticket on a single airline from Miami to Tel Aviv via Madrid."
3. "While Ms. Addi was solely concerned about her kids safety, there also should have been compensation involved for being involuntarily bumped off of a flight."
= Writing in passive doesn't come across as strongly. How about: "...safety, Iberia should have minimally offered compensation for involuntary bumping three minors off of a flight."
4. "However the Iberia customer service desk in Madrid told the kids that they could only receive a hotel voucher and not a compensation check for being bumped as they were all under 18. "
= Add a comma after "However" and after "bumped"
5. "They should have been checked in all the way to Tel Aviv when they were in Miami and checked their bags through to Tel Aviv."
= Better sounding: "How is it possible that these 3 kids were the last passengers to check-in for the Madrid to Tel Aviv flight? When the agent in Miami checked their luggage through to Tel Aviv, the kids should have been checked in for both legs, as well."
Also, foreign country sounds scarier than foreign city.
Poll