It would be "banʸimʸeedʸ" - [bˠanʲɪmʲiːdʲ] in phonetics. Or "bwinimeedʸ" - that's not expected from the spelling, but it is a variation.
The "w"-like sound [ɰ] in Gaeilge and duit is said without rounded lips. It occurs with ui, uí, aí, ae, ao, - basically wherever a slender vowel is pronounced after a broad consonant. It serves to stop the consonant from becoming slender before a front vowel, which is otherwise an automatic reflex for natives.
Or some recordings here: http://www.potafocal.com/x/teanglann.ie/?s=baineann
IPA renditions of Irish pronunciations are pretty meaningless unless they are restricted to a specific dialect, because there is often more than one "right" way to pronounce a word in Irish.
I'm not sure that you're doing anything wrong - this speaker doesn't consistently differentiate between díobh and díbh.
Táimid buíoch díobh
Bainimid na lucha díobh
Ní bhainim bhur léinte díbh
Baineann sibh bhur gcótaí díbh
Do they use de as a thing down there? I thought Kerry people used de and do as meaning being the same thing (with do as the basic form) and the respective forms of do and de were more to do with with words following broad or slender consonants.
That said, this Connacht woman sounds like she said daoibh to me (i.e. with a broad d sound).