The Priest may give the Sign of Peace to the ministers but always remains within the sanctuary, so that the celebration is not disrupted. 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 small number of the faithful near the sanctuary. According to what is decided by the Conference of Bishops, all express to one another peace, communion, and charity. While the Sign of Peace is being given, it is permissible to say, The peace of the Lord be with you always, to which the reply is Amen.
The whole thing is optional, period, though up to the priest. Sometimes a priest will say “Dominus vobiscum” and after the response “Et cum spiritu tuo” go straight into the Agnus Dei. Language in the missal also suggests it’s optional though many priests don’t realize this or just disagree with the notion that it’s optional. I’ll usually just nod to those around me unless it’s family.