Childcare is a cost that it is mandatory to divide, private school is not a mandatory cost. The answer in this case may depend on the definition of "private school." If it is a private child care center, and it is necessary for employment, then that will be called "child care." If it is a private elementary on up, then it is a separate cost and likely cost-prohibitive; therefore, if one parent insists on private school, they can pay for it. (Be aware, though, the court does not like changing children's school locations if it can be helped. )
If you are expected to pay 1/2 of private school expenses, then that should be specifically spelled out in the order and/or agreed upon between the parties. The mandatory costs are medical and childcare related to employment.
Family Code 4062 states:
(a) The court shall order the following as additional child support:
(1) Child care costs related to employment or to reasonably necessary education or training for employment skills.
(2) The reasonable uninsured health care costs for the children as provided in Section 4063.
(b) The court may order the following as additional child support:
(1) Costs related to the educational or other special needs of the children.
(2) Travel expenses for visitation. (Am Stats 1994, C466)
This is a family law question, you should hire a family law lawyer to evaluate this issue for you. It would seem that you have a valid point if your income does not realistically allow for private school tuition. The important issue is where was the child going to school prior and if it was public school, what now justifies the added expense of private school, when the limited available funds could be going towards child support for rent, food, clothing, medical insurance/bills, etc.?
Legal disclaimer:This message does not constitute legal advice and does not create an attorney-client relationship. Any statements are made for general informational purposes and do not constitute legal advice. No attorney-client privilege is created by this communication. Attorney is licensed in California only.
Yes, there are time limitations. Judges use "evidence". You should be hiring a lawyer, using the free services of the Office of the Family Law Facilitator at your courthouse, or assigning your right to child support to your county department of child support services for free representation.