If you have By-Laws in place you can remove a sitting president for a number of reasons. We had a situation where we almost had to do that, so I sympathasize with you, however, your school is not being done any favors by letting her remain president.
drdeb's right--did someone run against her or was this a case of "nobody wanted it it and now we're stuck". Hard to fire a volunteer. You may go to the next more active person and see if they are ready to lead even if they don't have the title. Sometimes someone of a lesser title becomes the defacto leader when the "leader" is not doing her job.
How did she get to be president again? It sounds like she doesn't even want the job, but if yours is anything like our PTO, no one is willing to step up to take the position. If anyone is available to replace her, ask her if she would like to be relieved of her post. If not, I guess you are stuck with her until next year, unless there is some provision in the bylaws for removing a sitting president.
I am a new member to our board this year. Our president is the same one from last year. Everyone else has stepped down from last years board due to this president. She has messed up fund rasiers, missed meetings, doesn't return phone calls, and this week we had open houses 3 nights in a row and we all took turns working, she didn't even show up. She said she was making dinner for her family. The last year budget is down $10,000 and when we asked people to sign up this year they laughed at us. She is a joke. What do you suggest????