I assigned a writing task to my student. She need to write an email to: apologize for her failure to keep the appointment, explain her reason,
and express she wish to make another appointment in an appropriate style.

Her writing is :
Dear Professor Brown,
First of all, I must apologize for not being able to keep our appointment. I do know that this is very impolite and must have caused you too much inconvenience. But unfortunately, on my way to your office, I got a call that my grandmother suddenly fell ill and had to be hospitalized. I do hope that you would spare your valuable time to meet me tomorrow afternoon in your office. And I am extremely sorry for that. Please accept my sincere apologies. I am looking forward to hearing from you.
Yours sincelerly,
Lily

First of all, (no 'secondly' follows) I must apologize for not being able to keep our appointment. I do know that this (It) is very impolite and must (repeat. There is a 'must' in the first sentence.)have caused you too much inconvenience. But unfortunately, on my way to your office, I got a call that my grandmother suddenly fell ill and had to be hospitalized(be sent to hospital). I do hope that you would spare your valuable time to meet me tomorrow afternoon in your office. (Could you spare me some of your valuable time tomorrow afternoon in your office?) And I am extremely sorry for that. Please accept my sincere apologies. I am looking forward to hearing from you.

Could you tell me whether my correction is right or wrong?

Thank you.