Meeting cancellations are sent out as emails with a specific outlook form so if your calendar were copied into the meeting request, you would have a record. The cancellation messages are deleted by default once you've acknowledged them but I think you can turn that off in Options.
In your case though, you won't get those since you are only looking at a shared calendar, the owner of the calendar will get cancellations for messages they didn't set up. Entries they originated have no record of deletion except that the calendar form will end up in the deleted items folder until that is cleared out.
One possible approach might be, if you are arranging meetings, to do it from your own mailbox and include the other mailbox as an invitee. Or alternatively, do it the other way around. Create the invite in the shared calendar but include yourself as an attendee. Then you get any cancellation message. Note however that it is possible for a user to suppress any attendee update messages.
The only other options I can think of either involve changing permissions to prevent someone from deleting things or writing a Macro to keep track of actions.
UPDATE: I think you will have to go old-school. Print off her schedule regularly so that you have a printed record of everything and then monitor her calendar closely.
The other thing would be to report the missing entries as a fault to your IT department. Don't tell them about your fears of course, but armed with the print outs push the problem to them. It is possible that they will discover her doing something wrong and then they get to make a fuss rather than you. If you do get evidence of wrong doing, plan on how you would blow the whistle on her but be ready to look for another job.
To be honest, if you don't trust her, you are really in the wrong role anyway - time for something new if you can - though I realise that might not be so easy.