[I am a mother of two teenage girls and have been in elementary education for pushing 20 years with 6 as principal.]
It sounds like your 2 yr. old is going through a normal stage. This is good. Your response will be critical for health maturation. It is important that you NEVER give a child what they want during a tantrum. When it 'works' for them they learn that screaming is an acceptable behavior. On the other hand, don't resort to sreaming back or physically punishing the child. Then they learn that is acceptable behavior.
It sounds like your daycare person knows what they are doing. Ride it out. If you need to move the child to a safe or calmer place do so with as little physical contact as possible. When the tantrum is OVER try to help your child find the words to express what they want. If reasonable help them get it. If it is not reasonable or acceptable be the adult, say no and stick to that.
Children who do not get firm and consistent parenting at various developmental stages lack the skills to be successful in school. Every year there are kindergarteners across the country learning the word 'no' for the first time.
Good luck and be strong. You will save yourself endless hours of grief later by being firm and calm today:)