OP Having decided to go to the school, I would personally let the school deal with telling the other parents.
I know people are very keen for you to report this and I do agree but I hope you can work with your daughter to help her to see this is best for her, to protect her from any future contact with the girl.
Bullying and controlling behavior dis empowers people, as you know I am sure, so you do need to empower your dd and let her know you are listening to her.
I would really leave it to the school to contact the other parents, this abuse happened while the girls were at the school togetyher, it is their business.
However, if you feel you must contact the other parents, please do tell the school first and then use whatever wording you wish to. So your wording is OK but in your shoes I agree to spell out what has been happening.
You do not need to change anything but I would consider...
"I have found out that your daughter has been messaging my daughter on social media and pretending to be a boy (called XYZ), she has said XYZ is (other girl's name's) brother.
Unknown to me, over a two year period these messages have continued with my daughter thinking she is speaking to a boy. Over the last two months (or over ABC period of time) these messages have happened daily..." (if true) "and have been controlling."
(Pretending to be someone else on line like this is often referred to as ' catfishing').
If true you could also say "The messages have been abusive or the control has been a form of abuse)" (I would completely say this is the case but you need to use words you and your dd are happy to use.
"I am not trying to stir trouble" You do not need to say this, but I would say something like...
"I am a concerned parent and you need to talk to your daughter about this."
I agree with previous poster, do not say "... it has ruined your daughter's friendship with my daughter and affected my daughter's outlook on friendships." We know it has and school will speak about this, just remain calm and cool, do not give any information that is not necessary (IMHO).
I would not end with a please, personally.
"Inform your daughter that she should not contact my DD in any way shape or form."