OK 1, thats the Seat Stay and a Side pull brake Plus a steel rim .

you mis used the chainstay terminology ..



to improve rear brakes , A: you should first buy . build a wheel with an alloy rim.

then fit a new cable and Housing the brake can be adequate ,

with a proper adjustment and New brake pads.

One thing I suggest is a bellows boot off a V type brake
between the side pull arms over the cable..

so a rainy day will not have much water getting in your housing and rusting the cable

towards the same end use a Stainless Steel cable.

you have a full overhaul in front of you ..