If your probation will be terminated on June 12th then you don't need permission from the probation officer to leave for your country on June 13th. If you want an expungement you will need to file a Motion for a Dismissal. You can do that on the 13th or anytime thereafter. You can always ask for early termination of probation but if you are in no hurry then you can file for your expungement as soon as you are done with probation. You can file the dismissal yourself or hire an attorney to do...
Yes, you can request a storage hearing through the police department. And yes 14602.6 applies but you can get the vehicle out prior to the 30 days if he was not the registered owner of the car. You say "our" vehicle so I am assuming someone else owns it.
The worst thing that can happen is they will file criminal charges against you for driving without a license which is a misdemeanor. They can also file charges for giving false information to a peace officer but I doubt it. The driving without a license is frequently reduced to an infraction.
Since there is no restraining or protective order in place you should be able to see your children. If your spouse is denying you visitation your only option is to go into family law court and see an order for visitation and this procedure is called an Order to Show Cause. However, it is unlikely a family law judge will give you UNMONITORED visits due to the pending criminal case.
Where is the second DUI? I do know that Ventura is one of the few counties where they place you on formal probation for a DUI. You need to contact an attorney to discuss your options and how you should handle this. I am very familiar with Ventura so you can contact me to discuss.