這個會不會影響父母探親？ probably not.

I do not think so.
But if you do fall into inadmissiable category, then there could be problems.

I have heard a similar case. The guy asked for a copy of the disposition papers from the court. And there was a letter in there from FBI which asked the court for all info regarding the case and the convicted. Fortunatedly, his terms was less than a year.