As I understand it, the new Anglican Rite of the Catholic Church keeps its services and married priests.
The Anglican Rite is modelled after the Eastern Rites of the Catholic Church. For example, I have a Lebanese Catholic friend whose church has married priests.
It is similar but different. The Eastern Catholic Churches are overseen by a Metropolitan or Patriarch. While they allow married men to become priests, the majority of the eastern churches only send celibate priests to serve in the US. That is the case, at least, in the Maronite Catholic Church. I am guessing that your Lebanese catholic friend is Melkite which has chosen to disregard the norms of the western church.
In the Anglican Rite model,
The Apostolic Constitution does not dispense from the provisions of the Code of Canon Law of the Catholic Church forbidding ordination of women and ordination of those in irregular marriages, but it does make provision for ordination of married former Anglican clergy to the orders of deacon and priest in the service of an ordinariate: "Those who ministered as Anglican deacons, priests, or bishops, [...] may be accepted by the Ordinary as candidates for Holy Orders in the Catholic Church″, Ordination to the priesthood in the Catholic Church is also open to married former Anglican clergy: "In consideration of Anglican ecclesial tradition and practice, the Ordinary may present to the Holy Father a request for the admission of married men to the presbyterate in the Ordinariate. This request is granted on a case-by-case basis, not as a matter of course but by exception: "The norms established in the Encyclical Letter of Pope Paul VI Sacerdotalis coelibatus, n. 42 and in the Statement In June are to be observed." On the basis of objective criteria determined by the ordinary in consultation with the episcopal conference and approved by the Holy See, the ordinary may petition the Pope, on a case-by-case basis, to admit married men to the priesthood as a derogation of canon 277 §1 of the Code of Canon Law, but the general rule is that the ordinariate will admit only celibate men. No married man may be ordained a bishop.
Not exactly. The Anglican ordinariate is a subdivision of the Latin Church where subsequent priests will be required to be celibate.
The Eastern Catholic Churches are in equal footing with the Latin Church in terms of canon law, and most have more autonomy than Latin-rite dioceses do.