So, if I understand you correctly, the icon of gOpAlasundari has the female form on the left (vAma bhAga - as in nAri vEsha dhara vAma bhAga), right, just like the ardhanAri form of Siva? Is there any reason why this preference for the left side?
I can't recollect the iconographic dhyAna shloka of gOpAlasundari, but yes, it is a commingling of male and female elements. I do not like the traditional depiction of ardhanariswara, wherein the union of the two is not organic, and looks like a composite photograph. Wouldn't it be so much more profound if the male and female features were distributed more naturally?
The wife is always accorded the position to the left of her spouse. The term vAmA has meanings like left handed, charming, crooked and an attractive woman. A lover is seated on the left lap - vAmabhAga-nilayA, vAmAGkastha etc. A child is to be seated on the right.
The Mahabharata has the story of how Ganga sought the king PratIpa, and went and sat on his lap. Alas, she said sat on the right side, and he said 'You are now like a child to me'. And she later approached his son Shantanu and wed him.
Also, which is the idol in mannArguDi that shows kRshNa as a cowherd, leaning against a cow?
This is the mannAr of mannArguDi. The utsava icon, whose nArI-vESa-dhara-vAma-bhAga-ness is indicated by the presence of mismatched earrings - one for each gender. I feel the iconography of this bronze is inspired by the exquisite Chola set of VRSabhavAhana that is now in the Tanjavur museum.