Should we hold hands during "Our Father"?
Here is the quote from church's CLARIFICATIONS AND INTERPRETATIONS OF THE GENERAL INSTRUCTION OF THE ROMAN MISSAL:
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: Not 11 (1975) 226.
As described above, the holding of hands during "Our Father" is from personal initiative, and it is not found in the rubrics. Thus, it is not proper to do so.
Here is EWTN's Q&A on this issue, answered by Fr Donovan.