I absolutely will not tolerate a company 'randomly' assigning me a shop without my applying for it or giving them specific permission to auto assign. That is just SO WRONG and flies completely in the face of our status as Independent Contractors. They want to do that baloney they can pay me a salary, share the taxes, cover me with workman's comp and unemployment and call me an employee. They don't get it both ways. So shops such as that they get back 'sorry, can't fit in my schedule'.
As for dates. If they ask me what date I can go (as they do on many of the SASSIE shops), I give them a date I will be available. I immediately note on my schedule the date and time and that it is 'requested'. If they assign me some other date/time, I will take it ONLY if it is convenient for me. I am certainly not going to reschedule other work when I left a time slot open for them. This is a business and they need to work with us in a business like fashion.