On her computer, why not just use Thunderbird on it? Or even outlook, or whatever she likes. She just needs to pick the software.
On her phone, or even yours, why the stuff with accessing Thunderbird through vnc. Just add the server to whatever mail app on your phones?
If you want a web based thing, roundcube or sogo. But Thunderbird is gonna suck the way you are trying to use it.
When a student goes to school, the school becomes in loco parentis and the student doesn’t have protection from school officials. Children, on campus, general do not have protection for free speech, protection from unreasonable searches or seizures, or really any of their rights.
The school, acting as parents, can restrict their speech, search their bags, and confiscate contraband.
The school can even waive most of the child’s rights even when dealing with law enforcement until parents arrive.