Normally we aspirate the needle/syringe prior to injection. That's how we prevent intravascular injections of lidocaine. Otherwise it would directly travel up to the brain and can cause seizures or other symptoms such as restlessness, disorientation, etc.
There are several possibilities in regards to the seizure. It may be due to an intravascular injection although from my understanding, the seizure would occur more rapidly since its goes directly to the brain quickly. If she had her complete treatment done and there was extensive work, they may have used a bit of lidocaine and it may have caused her seizure, especially since you noted that she took alot of shots. It may be that your daughter's tolerance for lidocaine is a little lower and hence, her dental work should be done in parts and broken up to reduce the amount of lidocaine needed.
THE SAME THING HAPPENED WITH MY SON TODAY BUT THE THING IS THAT THE DENTIST WAS HONEST AND SHE SAID THAT DURING THE INJECTION OF ANESTHETIC SHE ASPIRED INSIDE OF THE SYRINGE BLOOD SO NORMAL SHE GAVE MY SON 2.0%LIDOCAINE STRAIGHT INTO THE BLOOD VESSEL SO IT WENT STRAIGHT TO THE BRAIN.I CANT UNDERSTAND WHY THE DENTIST DOESNT LOOK BETTER TO SEE IF ITS ANY COMPLICATIONS AND ANY BLOOD AND THEN IF ITS SAFE TO PROCEED.?I AM A NURSE AND I GIVE INJECTION BUT MY DUTY OF CARE IS TO SEE IF ITS SAFE TO NOT AFFECTING ANY PATIENT IN ANY WAY.