So I sent the response email to my wife this morning as I wrote above, with the addition of the text in bold below:
"Dear Wife,
Thanks for touching base with me. E is the most important person in my life, so ensuring he is close and cared for is my top priority. I had made legal arrangements regarding your question, so if you haven't already been briefed by your counselor (it's been two weeks already), then you should be receiving legal documents soon.
- Alamo"
If she confronts me about it again, that I'm sabotaging her plans, I will let her know that this custody request was spurred by her infamous letter and the move to SC, but has nothing to do exclusively with keeping her from moving.