They wouldn't be forced to at all - it would be their choice to get an education for their children.
If there were no government schools there would be a vast array of private schools and parochial schools or even neighborhood schools or home schooling schools. There would be choices and I would be willing to bet there would be schools for parents children where the parents did not have enough income to pay for schooling where there would be scholarships to cover the costs of the schooling. Or even wealthy people doanating schools for children to attend.
I believe the choices made available through free enterprise would make it possible to have each child have an educational choice including having children being taught the profit making potentials for a lifetime of employment in "shop courses" like electrician - carpentry - auto repair - plumbing - carpentry where once you have those skill sets you are employed for life - even if you didn't attend some fancy ivy league college.