Ohh, you've hit all my 'hot buttons' - LOL at me!
Do you have any compelling reason to think that your DD 'in particular' is at risk for the sort of problems that are cured by single sex environments?
I 'hated' females at that age, and would have been really lonely without my guy pals.
Is your DD happy where she is? How does she do socially?
I pay for school because I have to, but I don't 'believe' in it. If there was a public school that would work reasonably for my son academically and socially, he'd be attending it.
If you are looking for votes, here's mine - homeschool latin and leave her in the public system. The academic fit sounds better and the 'willing to work with parent's factor' sounds better.
Best Wishes,
Grinity