Your D can’t come half an hour late to the cousins cookie baking because she had a college interview? She can’t miss her nephews pageant or recital?
Of course she responds to the email. Even if it’s only to offer up three time slots and to say “like everyone else, I’m feeling very time crunched right now. Many thanks for reaching out to me and I hope we can find a time to schedule a quick interview or phone call.”
It is always acceptable to be in a position where you can’t find a mutually convenient time. As a long time college interviewer (volunteer) I would have been moderately ticked off that a HS kid thought she was busier than I was (work full time, raising children, managing a household, community and volunteer work, juggling eldercare and frequent hospitalizations).
Really- a kid is busier than I am??? too busy to respond to an email?