Can I still travel with my family on cruise out of the country while on probation?
On Probation for DUI.

Ask your probation officer, but sometimes you can't leave the state if you're on probation.

Not a good idea without prior written permission from your PO. I doubt if they will agree to a cruise for you as you are on probation and under "punishment". So don't be upset if they don't let you go. You'll just have to wait until you are off probation to leave the state or go on a cruise.