CITI Ministries, Inc. is a national non-profit organization that provides "priests" to people for spirtual guidance. They administer the sacraments and perform weddings, but they are not exactly what a faithful Catholic would be looking for.
CITI stands for "Celibacy is the Issue", and refers people married "Roman Catholic" priests. These men claim to be "former priests" who decided to enter secular life to marry, and then act as priests on the side. Their "Rent a Priest" service claims that one-third of the priests ordained since Vatican II have abandoned their vows. They are legally married civilly and act as priests, but they don't wear clericals. Based on some promotional photos, they say the Novus Ordo and their liturgies are "ecumenical and welcoming."
This is a very sad state of affairs of how these men are conducting themselves. It is has been clearly stated since the 11th century by every Pope, including Benedict XVI, that only celibate men can be ordained to the priesthood. This is the Latin Rite practice, and has always been that way.
In the Eastern Rites of the Roman Catholic Church, married men may be ordained priests but in turn cannot be consecrated as bishops. The same holds true for the Eastern Orthodox priests, for whom their practices caused the Great Schism of 1054, where Rome and Constantinople split up their religion in two. The same also holds true for former Anglican/Episcopalian priests who have left the Anglican Communion and joined the Roman Catholic Church; if they are married, they cannot be consecrated to the Catholic episcopacy. So some former Anglican bishops in England who were married became Catholic priests, but they cannot be consecrated bishops. As a courtesy, the Pope named these new priests (for they have a special faculty to say the Anglican Use Mass) monsignori. I would not imagine that these men would have to put away their wives since the Catholic Church is 100% against divorce!
To that end, it is not the Church teaching to be married and having kids while acting as a priest. Jesus was never married, and the priest is supposed to be an Alter Christus (Another Christ).