Don't tell them until you know for sure that you are moving so it doesn't seem like you are really trying to get out of there. That's what I did when I moved 😉 hope this helped a bit
Tell them that it is for the better of the horse and that there is no hard feelings, but you need to move barns. You feel it is the right thing to do.
Calmly explain your reasons for leaving and try to have answers for any of the questions she may ask. If she still gets mad at you, it's her fault not yours. Your trainer should want what's best for you, even if it means you moving barns.