I wonder if you might want to start your own thread, because (sorry to sound cynical) you will collect quite a lot of 'whys'. And often the only answer is Crisis. My H did something very similar, in a similar time frame. After 6 months of silence, he popped up and seemed to think my brother would want to hang out with him, spend some time doing a shared hobby. When my brother had spent the last six months as part of Team KD, picking up the pieces. My H didn't even acknowledge what he had done. It seemed so odd and crazy at the time, but then, he keeps on adding to the pile of 'wait! what!?'. Treasur summarizes possible 'reasons' well. I would also add, it may be that he is so much in his weird hinterland bubble - the place where he is the good guy, doing good things, and you and the kids, you are resilient and doing just fine without him - why not have a friendly, helpful relationship with his MiL. Something like that aka a delusion. And if I was kinder, he may miss her and is unable to think beyond his own needs in this regard. I suspect, many of our spouses cannot bear what they have done, so they bury it, and try to present a nice, calm face of business as usual. But who really knows? I actually don't think they do.
You do sound like you are doing really well, but I expect you have your meltdown days like we all did/do. If you can try not to overthink his actions at this early stage, and have no expectations of him, you will protect you heart a bit more. Because, well, they are kind of predictable in their unpredictability at this point, and, I for one got dashed on the rocks a few times too many times.