You should get any travel approved by the judge to avoid further complications. Hire an attorney to put it on the docket and have them explain where you are going, when you are coming back, and the purpose of the trip. The state might object and the fact you have 2 DUI's isn't a good thing, but its better than violating probation and getting thrown in jail.
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Aside from the concerns about ensuring that international travel - or any travel out of your state for that matter - is acceptable to the court, be aware that you will likely not be able to go to Canada as their admissions laws are very strict when it comes to DUI convictions. With two of them, you are going to be waiting at least a decade in all likelihood before you can even try it. Seek guidance from the Canadian Consulate nearest you.
I am not aware of any other countries that prohibit entry with a DUI conviction on your record. However, you may want to take the extra precaution of contacting the Consulate for any country you plan to visit prior to making your travel arrangements. That is the easiest way to avoid trip-ending problems.
I am only licensed in the State of West Virginia. Comments offered in my answers are intended strictly for the purpose of sharing ideas that person asking a question may want to consider. Legal advice can only be given by an attorney licensed in your state and offered in the context of the attorney client relationship. No attorney-client relationship is offered or created by my answering this question.
Your current probationary terms may restrict your travel even to other states in the US, so make sure you discuss any possible travel plans with probation before you make any concrete plans. If your question is geared more toward the future when your probation is done, the only country you really need to worry about is Canada. They are very strict about barring anyone with even one DUI from entering their borders. After five year with just one DUI, there are ways to ask for permission to enter, but it is costly. Plus, you now have 2 incidents, so you might want to just cross Canada off your list of travel plans. Other than that, I do not foresee any problems.
Some countries will not let you enter if even you have a single DUI conviction (as Canada). Other countries will not let you enter if still on probation from a DUI. The only way to find out for sure is contacting the contries's embassy or consulate nearest to you well before traveling.
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