I studied anthropology, this (or some variation of this) is a pretty common thing cross culturally. from the perspective of someone from whatever culture your wife and her mom are from, it wouldn't really be the same if the MIL just came to your house periodically, because the whole point is that the woman who gave birth is in an extended family environment. if the MIL was just visiting your house it would remove a lot of the intimacy, and the social bonding quality, from this custom.

I think the MIL could have done a much better job of explaining this to you (instead of just saying "it's our culture, not negotiable"). if it is something your wife values, and it's really something she wants (rather than something she's doing out of a feeling of obligation), I think it is important to let her do this and work around it.