Can you review this e-mail i plan on sending to an old supervisor?

Okay, feel a little bit better having gotten that down on paper and out of your system? Good. Now delete it or save it somewhere that you can't send it accidentally. There are ways to express your disappointment at not having been chosen for a position and politely ask the coordinator if there's any possibility that you could be granted some insight into the reasoning behind the decision. Making umptions about that reasoning, airing every last one of your grievances about the process, and closing with completely insincere best wishes given the preceding accusations of disrespect are not among them.