Quick answer? NO
You cannot leave the country while on probation or parole. You have to petition the sentencing judge to have your probation modified if you want to make a trip outside the US, a probation officer does not have the power to grant a travel pass outside the US and its possessions.
When someone raises the question about traveling to another country where they have family makes me look to see if they are a full citizen. There is a bigger issue you might want to think about here, if you found to be in US on a green card (or similar document student visa, work visa etc) and are convicted of a felony you can have your green card revoked and sent back to your country.

