Holding hands during the Our Father has become commonplace, but it is an illicit addition to the Liturgy. Clarifications and Interpretations of the GIRM ["Notitiae" Vol. XI (1975) p. 226] explains:
". . .holding hands is a sign of intimacy and not reconciliation, and as such disrupts the flow of the Sacramental signs in the Mass which leads to the Sacramental sign of intimacy with Christ and our neighbor, Holy Communion."
112. QUERY 2: In some places there is a current practice whereby those taking part in the Mass replace the giving of the sign of peace at the deacon's invitation by holding hands during the singing of the Lord's Prayer. Is this acceptable?
REPLY: The prolonged holding of hands is of itself a sign of communion rather than of peace. Further, it is a liturgical gesture introduced spontaneously but on personal initiative; it is not in the rubrics. Nor is there any clear explanation of why the sign of peace at the invitation: "Let us offer each other the sign of peace" should be supplanted in order to bring a different gesture with less meaning into another part of the Mass: the sign of peace is filled with meaning, graciousness, and Christian inspiration. Any substitution for it must be repudiated.
I'm happy to say that during RCIA we were taught this, and as a result, my family are some of the very very few who do not hold hands during the Our Father.
The real point is diocesesan promotion of this practice, and if a diocese is promoting it, they are violating rulings by the Holy See raised in Doubts/Questions posed to the Holy See by proper authority. I could speak about the Diocese of Metuchen from years gone by, but the words I would type would break forth into flame on your computer screen rendering it a total loss -- and I don't wish that on my friends.
But back to the matter at hand: Holding hands for the Paternoster is illicit. Period.
Sorry for the delayed reply, but thank you for that reference.