Coach storming onto pitch

Had a feisty match today.
First goal the home coach storms onto the pitch to confront me about not calling a foul. He was shouting at me.

I sent off the coach there and then. I believe I’m correct in law although he believes it’s only a yellow.

I’m obviously filing the red card, but should I also add an extraordinary report that he came back at half time to talk to his team and at full time?
Or am I escalating it for no good reason?

You are correct that entering the field of play to confront an official is a specifically listed sending off offense for team officials.

Correct for sending off the coach. After being sent off, the coach must not return to the pitch. If they wished to speak to their team, this should have been done in the changing room at half‑time or full‑time. I would include this in an extraordinary report, as the coach should have left the field of play and not returned.”