You must apply and have your admission application accepted by a college or a university before you can apply with the United States Bureau of Citizenship and Immigration Services (USCIS) for change of status.
If you are admitted to the college or the university, you will be sent a Form I-20 by that university. Once you obtain your I-20 form, each of you need to file Form I-539 application to extend or change non-immigrant status to USCIS service center that has jurisdiction over your residence.
There is a $300 filing fee for each application. You will need to submit all applications with yours original valid unexpired I-94 arrival/departure records, your I-20 form, copy biographic date page of all passports, form I-134 Affidavit of support, and financial evidence to prove your or your sponsor have enough fund to support you and your children's expenses while you study full time in US. You and your children are allowed to stay in US while all your I-539 applications are pending at USCIS. All the applications will be considered abandon if all of you leave the US during the processing time.
You always have the option to visit a college or a university and talk to the international student adviser for any questions or guidance.