from what I read, j_s noted you had 5 complaints

1) not seated together
2) given incorrect info on luggage causing Japanese officials telling you to get your luggage
3) entering your wife as a child (which really went no where in your post)
4) your child getting sick while sitting alone
5) no wheelchair for your son.
6) apology accompanied by a certificate with poor T&C.

So, from the 5 complaints (yes, there are 6 but I have no idea if 3 is relevant), only #2 is AC's fault. Yes, it sucks that you received the incorrect info.

You probably had a few times to group the family together but failed to do so - a) at booking; b) at online checkin; and c) asking around you. I have never seen a case where families separated have not had people acquiesce to accommodate young children.

Also, did you ask anyone for a wheelchair for your child?

Often it pays to be proactive, esp when travelling with children. Asking will not hurt but it certainly can help you!

Perhaps if the cert is not to your liking, you may consider writing back and asking for miles. They may say no, but at this point, if you aren't going to use it, nothing to lose!