Can we live in the U.S. while our young kid attend private school?

Thanks for the reply, I totally understand where you're coming from. After extensive research and asking around, apparently there's a provision in the "U.S. Department of State Foreign Affairs Manual Volume 9-Visas" for your B2 visa that would allow you, as parents to live in the U.S. with your children who is considered a minor as long as the children are in the U.S. under the F-1 student visa. I hope this could make your life a bit easier. Below is what it says:

9 FAM 41.31 N14.4 Cohabitating Partners, Extended Family Members, and Other Household Members not Eligible for Derivative Status
(CT:VISA-2195; 10-14-2014)

The B-2 classification is appropriate for aliens who are members of the household of another alien in long-term nonimmigrant status, but who are not eligible for derivative status under that alien's visa classification. This is also an appropriate classification for aliens who are members of the household of a U.S. citizen who normally lives and works overseas, but is returning to the United States for a temporary time period. Such aliens include, but are not limited to the following: cohabitating partners or elderly parents of temporary workers, students, diplomats posted to the United States, and accompanying parent(s) of minor F-1 child- student. B-2 classification may also be accorded to a spouse or child who qualifies for derivative status (other than derivative A or G status) but for whom it may be inconvenient or impossible to apply for the proper H-4, L-2, F-2, or other derivative visa, provided that the derivative individual intends to maintain a residence outside the United States and otherwise meets the B visa eligibility requirements. If such individuals plan to stay in the United States for more than six months, they should be advised to ask the Department of Homeland Security (DHS) for a one-year stay at the time they apply for admission. If needed, they may thereafter apply for extensions of stay, in increments of up to six months, for the duration of the principal alien's nonimmigrant status in the United States.