To operate legally, your PTO really has 3 choices:
1) Under the school's umbrella, you operate essentially as a specialized committee of the school, probably devoted to volunteerism and fundraising. In this scenario, the school is the taxpayer entity. Ultimately all funds belong to them (whether or not they let you have a separate account) and they are responsible for all PTO activities. The PTO is not a separate entity. Whether or not taxes are owed, would depend on if the pre-school is a non profit or not.
2) Informal Association - With less than $5000 per year gross income, you can don't need to file the application to become a 501(c)(3) org. If you follow all the IRS rules as such and meet the "gross proceeds" test, you are considered a tax-exempt charitable og by default. You can still be independent from your school. The $5000 refers to EVERYTHING coming into your accounts, not just the "profit". (Important note -"informatal association" is not an IRS term, just one I'm using in this example.)
3) Formal 501(c)(3) charitable organization via Form 1023 application - you file an application with the IRS for this status. This makes you an independent non-profit that has credibility and donations to your organization are usually tax deductible. The application isn't trivial and there's a $750 fee, but many of us have done this. You may need to file a report with the IRS each year, but generally do not pay taxes. (Note, organizations pursuing this route usually incorporate with the state, which needs to be done first. Later, after getting the 501(c)(3) status, they usually also check into exemption from sales tax, which is handled by the state.)
I guess, technically, you could also operate as a regular business, file a commercial return, and pay taxes like a business. But I wouldn't imagine any PTO would do that.
What many do is -- nothing. They exceed the $5000 rule of thumb, but simply operate under the radar and either don't know the rules or just hope they don't get caught.