Can someone please give a reference to the following slokam?
aho yashode tava balakoyam grude gruhe
(39:23 in this video)
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This seems to be from the Rukminisha Vijaya, which is a Vaishnava work composed by the saint Vadiraja Thirtha in the 16th century. There's an online version linked here, and this specific verse is here.
aho yashodhe thava bAlakOyam gRuhe gRuhEthyuShNamapIha dhugDham
pibanna thApam labhathe kadhApi kimasya vavathrE jalashashirAsthe
[Part 3- line 53]
There's also this snippet, which is written in Hindi. You can only see the bottom half of the letters, but it looks to be the same line. All the online versions of the Rukminisha Vijaya include this line, I linked the one above because you don't have to download any pdf to see it.
Since Vadiraja Tirtha himself was the one who wrote the poems (rather than merely compiled them), it feels safe to say that it was he who wrote the verse too.
Hope that this is helpful! Let me know if you want a translation :)