I tried to do the same with a relay however I couldn't succeed. The readings are all over the place. Could there be a reason for this?
You have 80-90mA load per relay when energized ... lots of current draw out of those AA batteries just to enable a very light sensor load. How about trying a logic level MOSFET so you can turn it on with basically 0mA.
Also, most relay contacts don't work very well with light loads less than a few mA ... I bet you'll get lots of fluctuation just because of this alone.
The schematic link on this page advises to just power the sensor on/off with an output pin.
Possible, because current used by the sensor is <500uA.
Leo..