Let me guess, you feel like you've put together toys with more clear instructions!
If she does not accept the position of President, in away your former President is still Prez. Now if in the case that this is a second term for this person then what could be asked if she would be willing to stay on until a new Prez can be elected. As far as a meeting, I would start calling/e-mailing members to see how many can get together to hold a new election. Even if it means meeting at the park or coffee shop, otherwise this will need to be resolved when school starts.
Whatever her reasons are for quitting, please don't let anyone dwell on it. "stuff" happens and you get a shovel and clean it up and move on. I've got tons of shovels
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In the case of the Vice President, this is really a kinda "fill -in" position until the election can be held, unless she decideds that she could do this then she would assume the office and a VP can be elected. Now, I know it sounds and reads confusing but officers don't "move down" in roles. This is the resposiblity and in the duties of the Vice President to cover for the President.
Things like this happen and for this to happen now seems like the world may end
but your group will be fine. Better now than during the school year!