The confusion about whether your daughter has ADD or ADHD comes from confusion about how to diagnose this condition. The "official" diagnostic label is ADHD. The professional doing the evaluation, using behavior checklists, observations, and interviews with several people (parents, teachers, specialists, etc.), determines whether the inattention or the excessive movement (hyperactivity) is the primary feature of the condition in your child, or if both characteristics are present and overlap. It is important to know how the ADHD affects your child, so that you and your child's teachers can use the proper strategies to help her. If she is hyperactive, and that gets in the way of her learning, the school will have to do many things to structure the activities for success. The modifications will be different for a child who is inattentive, but not hyperactive.
There is also the question about language-based learning difficulties. Ask the psychopharmacologist to recommend someone he/she has worked with who specializes in the evaluation of learning disabilities. These two people can gather data from the school, go over past testing, and coordinate their findings and make a presentation to the school. This should put some of the confusion to rest and get your daughter's teachers and your daughter on the right track. Using a tutor to provide extra support is fine, but make sure that she's a part of the team. It's important that all of the people working with your daughter are following the same plan.