it feels more like a transitioning problem, along with tantruming because he isn't getting his way. i assume at home things are more flexible because they can be. the school can take steps to maybe help him accept when it's time to transition to the next activity. often, photo schedules for him to follow are helpful. he will be able to see and be prepared that they are going to something else. he also probably requires ample warning time. give a 5 minute warning, and a 3 minute warning. then, have a timer go off when it's time to transition. timers work well. perhaps you can start instituting use of a timer at home to get him used to it, and then let him help you pick one to buy and send to class. at home, use it to signal the end of something he loves to do to help him understand what it means.
Has your wife ever witnessed this behavior? Was he ever in daycare before this, or was he always with his mom? I don't realy think it's an anger problem, because children will show anger more where they feel the most comfortable, like at home with mom and dad. If you have never seen it, then I doubt that is what it is. Maybe it is more fear. If he has never been in daycare and is not used to being away from mom like this, maybe he is freaking out when he scenses they are getting frustrated with him? I would try to talk to him about it and ask him why. Talk to him alot about it. He will tell you eventualy. Just ask him why he was so upset, what happened when the teacher told him to go inside, and how did he feel at the time? Was he mad, sad, or scared?