Yes, the police can ask both you and the children to get out of the car. This most likely will not happen unless they have a suspicion that you could be carrying a weapon or they have probable cause and are going to search the car. You do have the right to remain silent and to the Fourth Amendment.
Arguing and resisting the police will not help you in the situation or in a court of law. Both you and the children have the right to remain silent should the police ask more than simple identification questions. You don't have to consent to anything.
The police can ask you to get out of the car at any time. There is not much reason to ask children to get out of the car, but the police can ask for that as well. They cannot search you, the kids, or the car without probable cause or without your consent. The police are ultimately able to do whatever they want/deem necessary, so arguing or resisting will not help you in a court of law should the situation escalate. Both you and the children have the right to remain silent and you can voice that you do not consent to a search if they are trying to search your vehicle. Should the police separate the kids or the kids unknowingly consent to a search (mostly kids below age 12), the judge will take that into consideration should a trial take place.