OP,
I am very familiar with your area as well as Horace Mann. I assume from your description that you are in the school district which is widely considered to be one of the best in the country. If sending your child to HM is not financially feasible, then you can’t do it. Your child will get a terrific education among her peers in her public school.
The difference HM offers from public schools is smaller class sizes, incredible course offerings, college counseling from counselors who have no guidance counseling commitments and have maybe 60 students each, probably 20 different AP offerings, incredible facilities,etc. Not everyone is wealthy, although a good number are and there are a number of “celebrity” kids. Kids who are not in the top 25% at HM can still get into very competitive colleges.
The colleges know that virtually all HM students are prepared to handle advanced college work. But, I bet that if you live in the public school district I think you do, that the colleges have the utmost respect for that school’s students, too.