I sometimes fly alone, and I would actually prefer to sit next to two children giggling at a movie, as opposed to having to sit next to, and slightly under a morbidly obese row mate, as I have had to do. On the particular airline in question, I had purchased a reserved seat, and was actually the first who chose a seat in the row, at the time I purchased my ticket.
Now, I have a question for those who think that the OP was "rude". Given that she didn't purchase EBCT, or whatever it is called on SWA, and she had 2 adults and 2 children, are you proposing that perhaps, she should have sent the 2 children in together first? Or, maybe the 2 adults, and let the children fend for themselves later? We are presuming that perhaps the man in question had a connection to make, and not the family? Or maybe, others think that one child had to sit with one adult, and vs versa. My son has been split from us at various times. One time in particular, we were on an airline that had 2-3 sitting. By coincidence, before the flight, we happened to find the people who were sitting across the aisle. How I reserved the seat is my son and I were on the 2 side, and my husband in the aisle seat across. My son decided that he wanted to sit next to his new friend (I think he was about 8 at the time). So, he did, in the middle seat, with the other mom in the aisle seat. He did great.