My DH is Maori and all our children have Maori middle names. This was my choice too though.
My MIL calls them all by their Maori names and introduces them to others by these names too. She says these are their maori names an their real names are their english ones.
It really irratates me
She even put only their middle names in the paper for their Koro's (grandfather) death notice.
Nobody knows them by their middle names so it was almost like they werent included in it. I knew they were but unless you knew us and our kids you would have thought they werent.

I try (and fail) to tell her that their names are as given on their birth certificates but she wont listen so I have given up and now choose my battles.

Families are hard work, especially in laws but I agree if you and DH feel strongly about it stick to your guns. Chances are your in laws will do what they want anyway