I'll add a communications technique that I find very helpful. Once you've decided what you are going to tell the coach, just repeat it whenever asked and add nothing even if ppl ask follow-up questions.
so
You: "Larla is going to start working with Coach Kristin, because we wanted her to have experience adjusting to different coaching styles."
Coach: "What? Why would you do that"
You: "we wanted her to have experience adjusting to different coaching styles."
Coach: Are you mad becuase x, y, z?
You: shrug . . . "we wanted her to have experience adjusting to different coaching styles."
Thien do the exact same thing when friends/competitors ask about the coach change.