Can probation officers search the entire house if an adualt probation officer comes to check on him n what rights do we have

You have all of your rights, you merely gave the rights to search away when you allowed someone on probation or parole live in your house.

Yes the PO may search without warrant your entire home.

I'm almost positive that while your son (the offender) is living in your residence, that gives DOC (dept of corrections) the right to search your home. I worked for DOC for a few years and I'm almost 100% certain that they do have this right. To make completely sure, ask to see a copy of his release papers (rules of conduct on probation) so that you can see for yourself exactly what rights they have.