I don't think sleeping with or without the dupatta has any meaning.they just shoot it as per convenience.the first time she shared bed with shiva after marriage she slept with her dupatta off, then she puts it on again sometimes.
It would have made sense if first she slept with the dupatta on and with pillows in between, then gradually got rid of the pillows, then the dupatta, then she would have begun to sleep on the same side.