Hi C.,
I see from your profile that you are in Ft. Lauderdale, but I don't know where so it is hard to give you concrete advice. I grew up in S. Florida and have been working in education for over 15 years now.
You have lots of options. First, for your older children, if you are not happy with the assigned public school, you can look at the Nova schools, which are public schools that do not have a district. You do not have to pay tuition to attend them, but you do have to apply and be accepted: http://www.broward.k12.fl.us/blancheforman/
Second, you can look at the magnet programs. These are also free public schools that you have to apply for admission. You can learn more here: http://www.browardschoolsmagnetprograms.com/
Third, you can explore charter schools. The City of Pembroke Pines has decided to use the charter school model in order to create the type of "neighborhood schools" many of us are accustomed to from our previous residences up north. You can find info on the charter schools here: http://www.browardschools.com/schools/charter.htm
I would NEVER decide to homeschool because you are afraid or concerned about the public schools. There are lots of options and you should explore them if you are using the homeschooling as a mistake. Homeschooling can be a wonderful and academically enriching experience, but it is a ton of work and doesn't work for everyone. You may want to reach out to some homeschooling families to get a better idea of the commitment that it requires.
I would be happy to answer questions if you want to message me back.
Cheers,
C.