A friend had some other friends staying at their beach house, and there were
"problems" with the power. This is third hand, so who knows what the real
story is. I may take a short beach vacation to see for myself.

it MAY be something like:

with both washer and dryer on, power went out. Maybe the main tripped. Or
maybe one side of the main tripped. Or maybe one side of the dryer breaker
tripped.

There is a lot of power consumption and maybe the line voltage was a bit
low?

How does one tell if a breaker is acting funny, like only blowing one side?
Or if the main is tripping a bit too easily? Do you just buy a few new
breakers and give them a whirl?