Autism is protected by the ADA but when we're are talking daycares they are not exactly held to the same standards as a school is. The teacher could argue that having the therapist in the same room with all the other children is a distraction. The directors response sounds like the nice way of saying we don't want it, or have to do it,

The real decision is how far do you want to push it, and what is that going to cause. If they don't want outside people coming in and you girce them, then they are just going to make things they can control difficult. This happens all the time. I am not arguing right or wrong it is more about what is best for your child and your sanity.

I would see if there is another daycare around that would be more willing to work with you.