Sun 24" Traditional Trike Help
The 24" Traditional trikes use the 19" support bar. The 23" versions are for aftermarket longer seat posts. So if that is the original seat post, and your mother is not extremely tall, then you need the 19". 

The 23" comes into play for taller riders so their knees are not smacking their chin and requires the use of a longer seat post than what comes with the trike.