Alternative support is a great idea!
I would sincerely hope that your T would not respond negatively. You need to have an option for when she is not available.
Plus, it is nice to be able to choose between who you want support from and think about where you can best get it, rather than only having one place you can go to for support.
I think that your email is more than ok; it's great that you are being assertive and proactive.