It's unfortunate that some parents don't recognize that paying for adjacent seating for their children is just a cost of raising kids. Doing anything with kids costs more money than doing things without them. Most airlines let you choose seats in advance, and sometimes those seats cost money. The cost of these seats is based on location. If you have to sit next to your child, then you have to pay to choose the location of the seats, just like everyone else. Seems pretty straightforward. I wish more airlines would make it clear to parents that there very well may NOT be adjacent seating if they don't purchase it in advance. It's not reasonable to expect someone who pre-planned and paid for a specific seat to relinquish it because you didn't pre-plan. If there isn't appropriate seating available for a parent, then the parent should choose a flight when there IS seating available. I hate to sound harsh about it, but the rules these days are you have to pay to get something. Gone are the days of seat assignments being free; that ended when folks complained about some passengers getting seats with more legroom (bulkhead or emergency row seating) without having to pay more.
Southwest has tried to mitigate some of this by doing "family boarding" between groups A and B. Kinda burns my butt that I have to pay for early bird seating or be online at a specific time to get a better boarding position but those with kids can just show up whenever and get a much better chance of having seats together (and yes, I know many pay for EB or do the 24 hour boarding position thing, but many also do NOT), but at least I know the policy and, if it's important to me, I can pay (EB) to improve the chance of my travel party having adjacent seating. We traveled this week and I was pleased to see, on all 5 flights, that the gate agents were clear to announce that a "family" consisted of ONLY 2 adults with children under a certain age. Doesn't matter how many kids, but only 2 adults, not parents and grandparents and uncles and aunts and and and...
Also, while grousing... 13 year olds can't sit by themselves on a plane? I bet those same 13 year olds go to the mall for the afternoon, completely unchaperoned, for example, but they can't sit on a plane "alone" with parents and flight attendants well within earshot? Heck, I had a steady babysitting job on Friday nights, four kids, from 6pm to midnight, when I was 12. Maybe do we coddle our kids a little too much sometimes, these days? (Yes, I know... fodder for another thread, for sure!).