Do you guys not keep trying to separate them, claiming that family and marriage is a distraction from God?
Of course not. Marriage, also known as the matrimonial covenant in Catholicism, is a sacrament. Catholics do not view marriage as better than celibacy, nor does it view celibacy as better than marriage. Both are of God, and some are called to a life of celibacy while some are called to a life of marriage.
From the Catechism of the Catholic Church:
**1620 Both the sacrament of Matrimony and virginity for the Kingdom of God come from the Lord himself. It is he who gives them meaning and grants them the grace which is indispensable for living them out in conformity with his will.117 Esteem of virginity for the sake of the kingdom118 and the Christian understanding of marriage are inseparable, and they reinforce each other:
Whoever denigrates marriage also diminishes the glory of virginity. Whoever praises it makes virginity more admirable and resplendent. What appears good only in comparison with evil would not be truly good. The most excellent good is something even better than what is admitted to be good.**
The entire section of the Catechism on Matrimony would probably be helpful for you to understand how Catholics view the sacrament:
scborromeo.org/ccc/p2s2c3a7.htm
What seems to be the issue for some Catholics when looking at the Mormon view on marriage is not that we don’t hold marriage in high regard (we do), but that it is tied to eternal life, and that to receive the highest eternal blessings, one must be eternally sealed to a spouse. To me this of course is related to the idea that God the Father has a spouse Himself, Heavenly Mother, and therefore to receive eternal life, to live the life that God lives, one must also be eternally married, just like He is.
So to emphasize, for Catholics, we believe that both marriage and celibacy are of God, and one isn’t better than the other. Some are called to one, others are called to the other. Both glorify God. For Catholics, your salvation is not tied to being married or celibate.
Then you would accept a married priest, as the Catholic church practiced historically and some Eastern rites still do?
Or would you view a married priest as inherently distracted?
The Catholic Church, as you mentioned, has married priests today, most being in the Eastern Catholic churches. For Roman Catholics, where celibate priests is the norm, we also know that this is a discipline, not a dogma, and that theoretically, Roman priests could be married men in the future.