We don't have the audio, but we still have Daenerys to help us:
This phrase seems to be the only time we encounter the possessive after the noun (muno engos nuhys instead of nuhys muno engos). So is it an acceptable syntax generally?
It is. It's always an acceptable variant; just rarely listed as the best translation.
Can this also be translated as: ""Valyrio ñuhys muño ēngos issa"?
I think this is also an acceptable translation.
Isn't that like saying: Valyrian is my mother's tongue?
Not, Valyrian is my mother tongue?
"My mother's tongue" would be "ñuho muño engos" if I'm not mistaken
My favorite scene in that series starts just before she says that. When she says. Zaldrīzes buzdari iksos dair!
"Nyke daenerys jelmazmo hen targario lentrot, yn anogar uepa valyrio iksan, Valyrio munos engos nuhyzy issa"
I think that's the whole speech