While I do think that parents should be given some leeway on a flight for fussy children, if they are trying to manage them, and I understand that circumstances may require a parent to travel by themselves with several children... in normal circumstances, at least some of the children would be old enough to manage their behavior, such that the parent could sit next to the youngest couple and have the older ones across the aisle from her (but still in the same row so that she can keep an eye on them).
However, Suleman is in the unusual circumstance of having eight children (well, fourteen, but let's speak of the eight toddlers) who are all toddlers at the same time. Usually somebody with eight children would have only a few who were preschool and under and enough older ones to help. In her case, she has to know that she's in an exceptional situation, and she needs to be prepared for it. She needs to hire somebody to help her on the flight, probably several someones, or she needs to make special arrangements with the airline if possible, or she needs to ask the studio to interview her in her home, or she needs to stop going on interviews that require a plane ride... she has many options, and taking eight toddlers on a plane with one 10-year-old daughter is not a good one. As somebody pointed out, airlines don't generally have eight seats together, not even in a single aisle. So, what, does she have two of them next to her, two across the aisle, and then the other four similarly with their 10-year-old sister? That's asking for trouble, and I think that another passenger is completely justified in asking her politely if she can quiet them, or asking a flight attendant to step in. For safety reasons along with desering a comfortable environment.