If the team is through the school, then I may be able to shed a little light on this for you. Our teams name was SIT (Student Improvement Team), so Jo is right, all the school's have their own names for this type of team.
The team is usually an administrator or two, a handful of teachers, the school counselor, and anyone else who makes sense to help kids at the school. I was a member for a few years, and helped rewrite the informational packet we gave the parents.
The idea of the team is to figure out what is going on with a kiddo, suggest accommodations, interventions, and make suggestions to the classroom teacher & parents. To help figure it all out, the parent is asked to give as much information as possible (like the last person said, pregnancy issues, delivery, family stressors, etc.).
Then the team tries to make the best plan possible for the kiddo. Sometimes the team, parents, or classroom teacher suspect a learning disability. To diagnose a disability, the school has to jump through a few hoops. The team has to do the first part (as mentioned above), have the teacher do several of the accomodation/interventions suggested by the team and measure those outcomes. For instance, ff the kiddo makes the same amount of growth in months as he/she was doing the accommodations/interventions, then a learning disability may not be the issue. So if your daughter made up some serious ground over the summer, than a learning disability was NOT the issue.
If a learning disability is still suspected (kiddo is getting further behind), then the team asks a child psychologist (most school districts have their own) to test the child. Depending on the age of the kiddo, this may take a few days. The psych will pull the student for short amounts of time in the school day to test him/her. They don't want to overload the student, and don't want them to miss classwork.
The other thing that is usually done is someone (our school counselor or another teacher did it) would come into the classroom to observe the student. The student never knows. The person will sit in the room with a notebook. The teacher usually says the person is there to watch the teacher teach a lesson. The observer will compare the student with another student in the classroom. He/she will count how many times the student seems engaged, asks questions, fidgets, etc. (The child is compared to another student because it's not fair if the student is disengaged and so are all of the other students because the teacher has a boring lesson --- or if the child is on the excited side of things and so are all of the other kids.)
Once everyone collects this information (and the team meets usually once a month), the testing will confirm a learning disability or not. If a LD is diagnosed, an IEP (Individualized Education Plan) will be written for the child, and services will be given based on the child's needs. If the child only needs help in math, then the child may get 30 minutes of extra help in the Resource Room (what the special education room is now often called) a day/or week. (The amount of time depends on the child's needs...this was just an example.)
What is important to know, if a child is on an IEP, the school will almost NEVER hold a child back a school year. She would continue each grade level, but receive extra help through-out the year.
A parent can always decline services, MUST be invited to the annual IEP meeting to discuss the next year's benchmarks and goals, and the child will be retested every 3 years. If the child tests at grade level at the time of testing, he/she will no longer require services (the goal!).
Students who qualify for services means that there is a good chance the student will receive the help he/she needs that as time goes on he/she will not need as many services as they go, and test out. Unfortunately, there are kids that are already working at or above their "potential" and will not receive ANY services!!! (This actually angers me.)
What jumps out at me if I were on the team. Your family has had lots of VERY stressful events. This would lead me to believe that your child has "lost opportunity." We used this phrase when a child lost days of school due to whatever, and/or when a child wasn't able to be there emotionally. Most kids in this situation make up a lot of time once they are ready, but need the individualized approach to go back to where they left off. (Tutoring is a great way to do this. Summer school is good, but it is still teaching the most recent concepts, not necessarily where she left off. She has some "potholes" in her concepts.
Now, if she were in my classroom, I would have suggested we start a case file on her to get the ball rolling. It takes MONTHS to do the above work to get a kid approved to be tested. I would have started this awhile ago, while we worked on accomodations/interventions that are measured and documented. I think that is why the director is upset.
PM me if you have any more questions. I'm sure I've left something out!
If you plan to work on her, my first piece of advice is to figure out her learning style and what she is interested in. Again, feel free to PM me, and I can help with some ideas. :)
Best of luck, mama. It is definitely unfair how one family can be hit so hard with very stressful events.