KV,
Panthuvaraali and Amruthavarshini have different colours altogether! how come you have bracketed them in same question? :-)
Panthuvaraali, Vasantha, Hamsanandi, Gujri Todi, Lalit, Sohini, Maarwa, Pooriya dhanasree.. these are the similar sounding raagas (for me).
As for your question on ARR's panthuvarali - Hai Rama in Rangeela is one.
Ruth Aagayi re is a fantastic song in that, but I remember reading that it is Pooriya Dhanasree.
I havent heard ARR using Amruthavarshini ever. But a small piece in the BGM of Robot does show a shade of that raaga for a moment, before changing its colour.