Honestly I've RTFT and it sounds like everything is sorted, everyone's talking, lessons learnt and mindfulness of DIL is in the bag so hurrah!
However, I can't help be struck by some of the hardline attitudes on here about MILs "transgression" in this instance.
Two people have (presumably) decided to have a baby together. They have decided on a parenting dynamic that suits them (presumably). They are adults and get on with it. The wider family seems pretty chill and supportive.
So I really don't get this endless analysing and hand wringing and expectation that either parent should be elevated or treated or recognised for their apparent contribution to family and society by virtue of having done what millions of people have done since the dawn of time.
Support and care and kindness from MIL should be a given because that's what decent people do, but having to tie herself in knots because she framed one on one time with her son in the wrong way and it's unfair on DIL comes across as a bit neurotic.
If a mistake is made, they can talk about it and do things differently to suit everyone's feelings then great, job done.
I'm just not really getting all the feminism / patriarchy / incubator rhetoric being hammered home.
At the end of the day, you choose to start a family, you then have to navigate and learn and adapt to how that goes with wider family and which battles are worth fighting. You're now an adult, and a parent, and yes, it's tough alot of the time, and yes, some aspects are unfair, and big problems and patterns of being de-valyed as a mother do need addressing. But I'm not seeing that in how the OP describes the situation and it's quite plain "lessons have been learned".(in fact the whole tone of things makes me imagine a world where fines can be imposed on MIL for such transgressions, and some posters probably would welcome that )
I think it's really sad that all sorts of relationships these days seem less and less natural and organic, and people seem to approach them with checklists of psychological analysis and immediate defensiveness before there are major signs of dysfunction. The world is not ideal, people are not perfect, big issues do need management of course. But this whole situation really doesn't fit into big issue territory at all IMHO.