It's your right to have your family with you. You must have compromised earlier for the sake of studies but it's natural to miss the family especially kids and I think you must apply for visitor visa at the moment which can be changed or extended later on.
Families of International student are not guaranteed a permit or TRV. Some get approved some don’t. They aren’t visitors so a spouse should be applying for an OWP and the children should apply for a TRV. You should also have a plan if they don’t get approval while you study.