I do agree the fact that, Technically Vridhakshatra did not commit any sin but virtually he did, The greatest Sin of any father is not bringing up his son with good culture and values. I could list several such mistakes of him for which he deserves such a punishment of killing his own son.
If I remember Vridhakshatra did not put any effort to advice his son for trying to abduct Draupadi.
Jayadratha was married to Dushala who was the only sister of pandavas as well as kauravas if the son is having an interest to abduct wife's brother's wife ( sister in law ) then I personally would blame the Father that he has not done anything good other than blessing his son for being invincible.
In Mahabharat Guru Vedavyasa did not gave many clarifications like this, because there are many situations in Mahabharath and Bhagavadgita ( which comes with in Mahabharath ) where Vedavyasa explains duties of a Father, King, Mother etc ....
One such example is you might also get a question saying what mistake did Dritharashtra did for loosing all his 100 kids, because in the entire story of Mahabharath I could maximum see the names of some 12 or 15 Kaurava names not all 100. Also not all 100 were bad to Pandavas and were not unfair . But the only mistake they all 100 did was supporting bad desires of Duryodhan.
Dritharashtra too did similar mistakes like Vridhakshatra, he allowed his son's Dhusyasana and Dhuryodhana to disrob Droupadi . That's a biggest sin ever, So he lost all his sons, infact in few versions of Mahabharath Vikarna and Yuyutsu who are brothers of Dhuryodhana objected for this act. But Dritharashtra did'nt so he deserved to loose all his children and lead the most sorrowful life after the war .
So to conclude my explaination according to our heritage Father plays a very serious role in bringing up the children ( this too comes in Mahabharath look out for Yaksha Prashna scenario in Aranya parva ). If Father ignorant of son's growth he deserves to be punished.