You could suggest that she set up a gmail account specifically for communicating with youall if she's not willing to share her primary address.
I agree with this. It's what we've done... we actually set accounts up under my step-daughter's name so both parents access the same account rather than setting up any kind of sharing of their own accounts.
Parenting four little monkeys (11, 8, 6, and 4) with the love of my life. Making it up as I go.
I was going to suggest gmail as well. Otherwise I suppose you could try setting up a family site (like myfamily.com or something like that) just to use the calendar feature in a password protected environment.
We use google calendar to track things pretty religiously, but we've never shared it with DSD's mom. She has on an again/off again internet connection, usually depending on her relationship status, so it didn't seem like the most reliable idea.