All these comments about what these sounds mean in different languages and dialects is not very useful, since the human throat makes certain sounds which mean different things in different languages. There are also lots of dialects, so it's a bit pointless saying x means y in whatever language if it's not the right language.
Getting cross about nonsense words is ridiculous. Babies and small children babble. It is good for them, and they soon learn which sounds are meaningful, and which are not. Even if they like the sound of their nonsense, so what? My grandmother's nickname for all us grandchilden was based on a mispronunciation by the eldest grandchild, and we always felt as though it was even more of an endearment as a result. So much so that "nana" and "nanny", as names for a grandmother, leave me utterly cold.
OP, if you are the primary carer, and using English (and if DH is, too), your DD is probably learning English first, and even if she learns a bit of something else on the side, why shouldn't she? Small childen are good at differentiating between languages, and an early start is best for helping her get it all sorted out.
Another matter to consider is whether your MIL is actually comfortable speaking English. It would be a shame to restrict her to communication in a language in which she sounds illiterate and inarticulate. By the same token, you surely don't want your DD to hear "incorrect" English, either, do you? 
If you have other issues with your MIL, fair enough, but this is the wrong issue to fixate on.