WOW what a crazy roller coaster ride. Did your agent tell you before you went on the gosee that you'd be expected to leave for 3 days on short notice? That would have helped, then if you had known maybe you would have turned down the gosee, or already arranged childcare just in case. My dd's agent always lets us know when and where a shoot will be when she calls us for the go-see. That way if we're not available for the shoot, then we don't waste our time (and the client's) going to the go-see.
Modeling can be crazy like that but I must say we have never been put in that position. Some of my dd's bookings have been on very short notice, but none of them required us to leave town for 3 days! And I've almost always been able to bring my son as a tag-along if I couldn't find a sitter. Modeling can be very competitive. Like you found out, there are cute kids lining up on every corner to take your place if you can't take the job. But overall my dd and I have had a fun, exciting, positive experience.
That's great that your son got booked, though! That is a good sign for his future success. I went back and found a thread called "realities of the industry" and bumped it up for you. It is in the top "getting started" section. I think the advice in that thread will help you! Good luck and much success to you and your son!