This is what I drafted to send them. Any thoughts? This has been extremely helpful guys...
edited for brevity
...I am very sorry to say this because Player is a very sweet girl who we enjoy coaching, but we will not be asking her back for the 2015-16 season. Dealing with your constant complaints, accusations of unfairness, and brazen confrontational behavior in front of other parents/kids is something we just do not want to take with us up to 12U. Player is of course is welcome to finish the season out with us, but we wanted to give you enough notice to start looking for another option for her for next season.
Too verbose. If you're going to do it in an email (and I wouldn't), keep it short and blunt, no wiggle room for arguing:
"Dear Parent, this email/letter/whatever is to inform you that we will not be asking Player back for the 2015-16 season. Your behavior in front of other parents and players exhibits poor sportsmanship, and is not something we want to take with us to the next level. We wanted to give you enough notice to start looking for another option for her for next season."
If I was doing it, it would be in person and I'd cut ties immediately.