If she's in the hospital she shouldn't be leaving Thailand she should be getting the extension in Bangkok. The hospital should be giving her all the information she needs and taking her to Cheng watana.
Like I say with friends and people going to India.
Just tell them you're a tourist. Who cares about income and other things like that.
Show them you have money, you don't have to show them where it comes from.
If you want to come to Thailand and stay longer term, get the 60-day tourist Visa, which you can extend for 30 days towards the end. But if you like it after one month then start looking at a long term Visa.
What a stupid system it's electronic! The "system" should not let this happen. Or the system should be able to be approved by any Consulate. It's not like LA or DC can't get the same information about you as the Chicago one.
When it was geographic of course it's better that way but it's electronic!
I know a 43 year old who was in Vietnam got a retirement visa OA approved through DC because he used his USA address. He's entered Thailand twice already on this visa.