I don't think your sister's palm is an areca, it looks more like a phoenix reclinata (senegal date palm...same family) - I think.
As far as your areca, I would keep trimming the unwanted seedlings/suckers. Eventually they make beautiful specimens.

The other day I saw the thread about "maintenance" of the areca and was a bit puzzled.

Other than sticking to a feeding program to keep the color, this is an easy plant.

And a great screen to block out your neighbors.

Why are you fighting its natural growing habits ?

If you want the "typical palm" look , there are soooooo many choices other than the areca.

Wet dry. sun shade , this is the best bushy palm you can have.

Oh, did I mention that you can block out your neighbors ?

I think its a reclinta as well.

It appears I was comparing apples to oranges. Both specimens are quite possibly 30 plus years+ old. I always thought my sister's palm had been maintained, whereas mine had been planted and largely ignored. Thank you for identificing my sister's palm, floridays and chuck.

Jupiter, I appreciate your input, too.