[Dominick]

lay extraordinary ministers of Communion are not authorized to give liturgical blessings

This is correct, absolutely correct. I may bless my children, as a father I am commissioned as the head of my "Domestic" Church. A stranger has no such commission.

I usually take my young daughter around and for myself to take communion from the Priest, and she gets a proper blessing.

[te lucis]

I may bless my children, as a father I am commissioned as the head of my "Domestic" Church.

Interesting. I've often wondered about this. Is there a source for more information? As parents, my wife & I trace the Sign of the Cross on our childrens' foreheads, but this is something entirely different from a blessing one would receive from a priest, no?

As far as the topic of the thread, we go to the TLM, and thus have no such worries about some layperson "giving a blessing" by patting them on the head, with what they are supposed to believe are particles of the Blessed Sacrament on their fingers. Our SSPX priest does bless children at the Communion rail by silently making the Sign of the Cross over them.

But suppose it happened that Sister Pat "blessed" your child and you, arriving back at your pew, noticed a Particle in his hair? What would you do?