See:
Entry to the U.S. - Denied entry of LPR convicted of a crime when reentering the U.S.
Apparently even if you are convicted of a crime it's difficult to be denied re-entry.
You haven't been convicted of a crime so I don't think it's an issue for you.
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Can a Lawful Permanent Resident (LPR) be denied reentry into the U.S.?
Lawful Permanent Resident's (LPR) convicted of certain crimes cannot be denied reentry into the U.S., although they will be referred to an Immigration Hearing to determine deportability.
Once a determination of deportability has been made, the LPR status is revoked, and a deportation order handed down. Once such an order has been issued, a former LPR would not be allowed entry into the U.S. after any subsequent trip out of the U.S. unless a Waiver of Inadmissibility (I-192) is granted or if a Port Director approves a temporary parole (usually for humanitarian purposes).
The legal grounds for removal of LPR status are found in the Immigration and Nationality Act,
Section 237.
Some of the most common grounds for revocation are: Fraud, theft, rape and related crimes, assault and battery, money laundering, drug dealing and alien smuggling.
If the conviction is of a particularly serious nature, it is likely that you would be detained until the date of the hearing.