Regarding children standing around the altar, there is no place in the rubrics that allows for this.
As for the position of the priest’s hands during the Our Father, the GIRM states:
“After the Eucharistic Prayer is concluded, the priest, with hands joined, says the introduction to the Lord’s Prayer. With hands extended, he then says this prayer together with the people” (#152).
As to when “For yours is the Kingdom . . .” is prayed, the GIRM says,
"[font=TimesNewRomanPSMT] After the Lord’s Prayer is concluded, the priest alone, with hands extended, says the embolism *Libera nos *(Deliver us). At the end, the people make the acclamation *Quia tuum est regnum *(For yours is the kingdom)" (#153).[/font]
[font=TimesNewRomanPSMT]As to the procedure for the sign of peace, the GIRM explains,[/font]
[font=TimesNewRomanPSMT][font=TimesNewRomanPSMT]"Then the priest, with hands extended, says aloud the prayer, *Domine Iesu Christe, qui dixisti *(Lord Jesus Christ, you said). After this prayer is concluded, extending and then joining his hands, he gives the greeting of peace while facing the people and saying, *Pax Domini sit simper vobiscum *(The peace of the Lord be with you always). The people answer, *Et cum spiritu tuo *(And also with you). Afterwards, when appropriate, the priest adds, *Offerte vobis pacem *(Let us offer each other the sign of peace). The priest may give the sign of peace to the ministers but always remains within the sanctuary, so as not to disturb the celebration. In the dioceses of the United States of America, for a good reason, on special occasions (for example, in the case of a funeral, a wedding, or when civic leaders are present) the priest may offer the sign of peace to a few of the faithful near the sanctuary. At the same time, in accord with the decisions of the Conference of Bishops, all offer one another a sign that expresses peace, communion, and charity. While the sign of peace is being given, one may say, *Pax Domini sit semper vobiscum *(The peace of the Lord be with you always), to which the response is Amen( (#154).
[/font]As for holding hands during the Our Father, “The Holy See has not ruled directly on this issue. In response to a query, however, the Holy See stated that holding hands ‘is a liturgical gesture introduced spontaneously but on personal initiative; it is not in the rubrics.’ (Notitiate II 226,DOL 1502 nR29). For this reason, no one can be required to hold hands during the Our Father” (*Mass Confusion, *Jimmy Akin, p. 161)
I hope this clears up some of the confusion.