@La***
, okay, until you know whether the school you're attending will or won't help with sponsoring your family on Non-O visas and extensions you're just guessing on what to do.
If the school won't do it, your options are limited.
Get everyone 6 month METV <-multi-entry tourist visas which you could wring almost 9 months of stay in country out of with border bouncing (yep, if the kids are on this type they'd need to border bounce to be legal) .
Get your spouse a 6 month METV and let the kids overstay.
Those are the only real options you have if the school won't help you secure dependent visas and extensions based on you being a student.