An employment application is no place for half-truths. You have to understand that private schools have a fiduciary responsibility to their clients. They cannot afford to hire somebody who might jeopardize the school's reputation or, worse yet, cause harm to students. That is why it is so important to answer all the questions on an employment application truthfully.
Background Checks
Most private schools will use a service to do background checks on any potential new hires. They will not run the background check until they have interviewed you because background checks are expensive. That's another reason why you need to be truthful about anything in your resume which will arouse probing questions and nix your chances of even being interviewed.
What the background check really examines is your criminal and credit history. If you were charged with a criminal offense or have bad credit, that will show on your background check. Take the offensive and point out that your credit was destroyed by huge medical bills as a result of your mother suffering from Alzheimer's. Don't be creative. Just tell the truth.
Expect a drug test at some point in the hiring process. Since views about pot and even alcohol vary widely from one part of the country to another, make sure those tests come out clean. If you have been prescribed a controlled substance that will show up in a drug test, mention it proactively and file a copy of your doctor's prescription just in case