Though I'm usually flying solo, I've observed the dance at several airports: In general, if you're polite and they aren't running around with their hair on fire most agents will expend some nominal amount of effort, particularly if you have very young children amongst your group.

Though the specific reaction/tone is very much airport dependent. ORD and EWR tend to skew to "Shove it and sit down" in my observations, LAX and DEN tend to be a little bit more accommodating. [Disclaimer: Non scientific sample and sample size]

If they're short staffed/dealing with oversells/misconnects/a mile long standby list/... they may hold your BPs as a courtesy in case anything magically happens but they are markedly less likely to expend actual effort (such as paging passengers and asking if they'd be willing to move).

Your best bet is to be proactive -- watch the setmap daily before departure and several times once you're within T-24 of flight as movement will occur (SDCs, Silvers moving to E+, elites moving to the F cabin if a CPU-eligible flight, misconnects). You can re-check in from the app to grab better seats if/when they open up.