Thank you for your question. I look forward to working with you to provide you the information you are seeking for educational purposes only.
Being on parole in general is pretty much no different than being in prison in the fact that the person has to follow the rules and the parole officer can make the rules and the parolee
has very few if any rights legally. For sex offenders it is even worse because on top of the parole rules, there are very harsh sex offender rules as well that seem almost unreasonable, but are the law nonetheless.
First off, while the Parole officer has jurisdiction over your son, if your son is in a place and the girlfriend shows up unknown to him then your son's actions of leaving as you described above would be the proper actions and no court
or parole board
would uphold a revocation over a chance meeting, especially in a small town and where your son left immediately.
Second, the parole officer CAN make him not see her or be around her or the children, that is within the parole officer's power, so while he is on parole he has to abide by the parole officer's requests even though the prior parole officer allowed it, the new one can still refuse to allow it.
Your son is just beginning to see the problems sex offenders have way beyond even other convicted felons. If this is a small town, your son needs to consider seeking permission to move to a town where he is not known, because in small towns it is even worse for sex offenders as everyone talks. Legally, the PO has all of the rights as long as your son is on parole, so your son has to follow whatever the PO says even if he believes it is unreasonable.