Actually, if I were your boss, here's what I would do.
First, I'd have a confidential conversation with HER boss, to say, "I've noticed this pattern of her linking both of us in--it's coming across like she's tattling to you and to me about rescheduling meetings, etc. So I just want to make it clear: I think my employee is doing the right thing--I'm happy with how things are. My policy is that he needs X days' notice to reschedule his shifts.
"And I'm tired of always getting looped into this. So here's what I'm going to do: I will reply to her directly without emailing everyone. And then I'll ask her to pick a time that fits with my department's coverage."
And then at the next email, I'd reply directly to her and say, "My department is not staffed to have meetings on those days. You will need to schedule your meetings on Tues, Wed, or Thurs. If something is so urgent that you can't fit it in on those days, please email directly to me to request that I change the schedule. However, I've noticed that you frequently cancel meetings, so it's hard to see things as being that urgent. You will need to explain why I should change my department's schedule in order to accommodate you.
"Should you wish to hold this meeting on Tues, Wed, or Thurs, you may email Tom directly."
And I would *not* loop Tom in, nor her boss. In a way, I think that actually would be more powerful.