I like both Susan and Shira's answers and have a few questions to ask the teacher.
First, how does the teacher address children about using the bathroom? I am a preschool teacher and after *years* of accidents, I know now that kids need to be TOLD to go use the toilet, not ASKED. For so many reasons (busy playing, asserting their own authority, not enough experience with bodily cues), when we ask a child "Do you need to go potty?" they just respond "No" and keep on playing.
Does the teacher have a system to support 'saving' the child's work/toy until later when they have to use the bathroom? I have found that, when a child is resistant to using the toilet, there's often a concern--most commonly, they don't want another child to take their toys or move/rearrange something they have constructed, etc. With my group, I have options for this: they can put their toy up in a safe place and I reassure them I'll give it back OR I cover their work with a light scarf, which my group understands to mean "leave it alone, it isn't available". I also have children who really want me to wait before starting a story so they can take a needed bathroom break, so I am happy to lead the group in a song or two while we wait. Getting to the root of the child's concerns is important, and being flexible helps.
I'd also want to find out how accidents are handled. What sort of support for toilet learning is available to the students and teachers? The University of Michigan has a great webpage for early childhood ed students on toilet learning, and I have found this approach to be highly effective and more thoughtful than some more traditional toilet training models. Google "Toilet learning" to find out more. The word "angel units" will be somewhere in the URL, if I remember correctly.
Not to contradict your teacher, but I do wonder if perhaps she's just got no time to 'deal with' the accidents? Having peer models is important, but I think there's value in knowing that sometimes even your models make mistakes. Accidents are just that--mistakes, and teaching children that everyone has challenges is a pretty real life lesson. No one's perfect. I would also discuss this with the director/principal and ask about written policy. Suggest to them that you will continue to work with your son, but for the sake of consistency in his life, you'd like to know exactly what sort of expectations your family must meet. See if you, the teacher and head administrator can develop a plan with goals and deadlines together. (He's 3! They need to cut him a little slack!)
If you check out the Mamas On Call website, they recently posted a short article on using pre-programmed sports watches which go off at intervals to remind children to use the toilet. There's more on medical issues in the article. I found it to be very intriguing.
I personally deal with accidents very matter of factly at my preschool and while children must be 3 to attend, I don't have a toilet-training requirement. I've heard of some daycares that have actually had kids excluded from care until they were successfully staying dry before returning. I find this attitude very disrepectful of the emotional consistency young children need. It takes a lot for kids to get used to the rhythm of a new school or caregiving situation, and then to jerk them around based on performance at such an early age? Sheesh...how will this sort of pressure and inconsistency in the child's life actually be helpful?
Okay, I'll get off my soapbox here. I hope that this works out for the best. It's likely of value to both of your sons to be with each other during the day. I think, personally, that the teacher could be more understanding of the changes in your son's life and that he's hopefully just had a minor stumble of a week and that this is not a major hurdle. The teacher and child are just beginning to know each other, and it might be worthwhile to share what works at home with her. If she's still unmovable on this--well, your son might be better off with someone who is more comfortable and relaxed in this area. Sorry--what a hard way to start the school year!