Kerri called the Kuwaiti Consulate in LA as soon as she could to find out what she needed to do. They told her they had received the fax and that all they needed from here was a medical "exam" (any doctor would do, just a general good health check), Rowan's immunization records, and a police report on Kerri.
Others at work told me I needed to send one of the 2 copies of the visa that the immigration office gave me, so I had Kerri call the consulate to ask, and oops, yes, they need that too. I was able to fedex them over pretty cheap (6KD) using 2 day shipping.
The part that may delay things is now the police report, which apparently takes 7-10 days. If it does take longer than Kerri's leaving date, we'll just have to change the tickets which luckily will only cost $25 each.
We're almost there!