Slow AF is a BIG problem when shooting kids, he's going to miss a lot of shots, trust me it's better to have the shots in focus on the kids, even in APS-C then out of focus with a full frame, and with a sharp background!
I don't disagree.
That's the crux of the matter. He's mostly shooting under 7 yo kids, which is no easy task, and certainly not something that inexpensive DSLR can achieve, which is why I recommended him the camera with the second best AF available, the a6400.
He might just love the APS-C and keep using it for a very long time, at least until he finds a FF with the same AF abilities as the a6400, which so far only the a9 can beat.
I think the obsession with "upgrading" is counterproductive. He should establish a budget and figure out what system works for it and his needs. It may not even be Sony E. Dollars go very far in the DSLR world, and frankly the weight/size differences are not that massive, especially when you factor ergonomics in. Outside of IBIS, which admittedly can be huge depending on what one shoots, and live view performance, which again can be a game changer/deal breaker (def is for me), I don't see a huge advantage in getting an A7II over something like a D750 or 6D2, especially when you factor lenses in.
That's the thing, he doesn't need to upgrade, but if one day he wants, he can, it's just a bonus. I think the a6400 will satisfy all his needs for a very long time. I don't recommend the a7ii nor those DSLR, because of the kids issue, that I mentioned above and that was mentioned in the OP's first sentence.