Do you have any sort of employment contract, employee handbook, or company policy regarding changing shifts? The first thing I would do is try to find something in writing that states when/how an employee can be made to change shifts. If there is no policy, though, and you don't have a union, you might be out of luck in that respect.
A meeting with the DON is a great idea. An impartial third party rep would be good as well. Do you have an HR department? I would explain very simply that you are not able to switch to the day shift and you need to be put back on the schedule for your original night shift. Offer to come in for a few hours during the day (get a baby sitter) 2-3 times per week for the "training" that she thinks you need. If she refuses, ask to be moved back to nights until her boss returns from vacation so that he can be made aware of the situations. If she also refuses that request, let her know that you will be contacting her boss about this and when he returns from vacation you will be scheduling a meeting where all three of you, (as well as someone from the corporate office, if needed), will discuss the matter again. Write out your statement (that you cannot switch to days, request to be moved back to nights, and have offered to come in for training during the day) and ask her to sign it in the presence of your witness.
If there is no policy found and the meeting doesn't go well, I would definitely escalate up the chain. Is the boss going to be happy about being called while on vacation? Absolutely not. But whom will he be more upset with? The employee who felt she had to call because she had no other recourse... or the DON who created the situation in the first place? If you can send an email to the boss, that would be my first choice of communication. Then a phone message with a short message such as, "I'm so sorry to bother you on your vacation. I really hate to have to call, but I truly feel I have no other options at this point. ____ DON has informed me that I have to change from 12 hour nights to 8 hour days and has not given me a satisfactory reason for this change. Due to child care conflicts, I absolutely cannot work day shift and if we can't get this straightened out, I will be forced to find another job. I really enjoy working for you and X facility, and I don't want to leave. I am willing to wait until you return from vacation, but it's very important that we address this together as soon as you return. Thank you. Again, I apologize for interrupting your vacation and hope your last week is very enjoyable." That will inform him of the situation, let him know you're serious and the matter needs his attention upon his return, but doesn't obligate him to get involved right away during his vacation.
Hopefully you have a good enough relationship with this boss and your facility as a whole that you can overcome this situation. I know there are two sides to every coin, but from what you described, it does sound like the DON is on a power trip and making some big mistakes. Be calm, be professional, get everything in writing. Good luck!