> If they are parents, they can bless their children.
Correct. Don't forget godparents can bless godchildren as well.
> For anything else, one should have a priest do it.
This is not accurate. The laity can perform any blessing found in the book of blessing that does not require a priest or deacon.
To make this easier, there is a book called Catholic Household Blessings and Prayers published by the USCCB that contains all the blessings the laity can do.