I've heard of this before-that the books of very small children were sometimes not stamped. If the I-202 and information above doesn't work for you, if you might do the following: You say you crossed as a family, so would be possible to get notorized copies of *everyone else's* passports in your family that crossed with you as well as affidavits from each of them stating who they are in relation to you, describing what day you all crossed the border, and testifying that they were with you on that day and you all crossed together with inspection? It seems a bit harsh to keep a 5 year old accountable for making sure he has his own I-94 stamp if they can't find your records, so I was thinking the above documentation might suffice.

I WOULD NOT leave the country to deal with this, however. I would submit the above information with the I-130/I-485 etc.