This is normal behaviour of a 27 month old. It has nothing to do with the fact that he has down syndrome. Although the daycare will make a big deal out of it because the child does have down syndrome.
This is an excellent opportunity for the daycare to teach all the children that biting and pulling hair hurts and is not a nice way to treat each other. For children of this age, a lot of pictures can be used to talk about how to treat people. When it happens with any of the children, not just the individual with ds, give both children time to calm down, talk to the children who did the offense about how they hurt the other child and have them hug and say, sign, or use a picture symbol to say sorry.
This is not for the mother to fix at daycare, it is for the daycare to fix. The mother can only work on it when it happens at home.