Describe the relationship between Calpurnia and Antony in Act 1, Scene 2 of Julius Caesar.

The play Julius Caesar by William Shakespeare begins on the day of the Lupercal.  Originally, the Lupercal had been a feast of fertility of the animals, celebrating the spring when animals bred and gave birth to their young. On this day, February 15, 44 B.C., Caesar and his wife Calpurnia have come to watch the race. The Lupercal has changed in time to represent fertility for women as well. 

Calpurnia and Caesar were married in 59 B. C. Calpurnia was a 16 year old virgin at the time of their marriage and was Caesar's third wife.  They loved each other despite Caesar's dalliances with Cleopatra and their illegitimate son. 

Calpurnia depended on omens and portents to supervise her life.  Highly superstitious, she believed that her dreams foretold the future.  Thus, in Act II, Scene ii, Calpurnia warns Caesar not to go the Senate.  This has been reported by Plutarch as an actual event between the couple.

On this day, Marc Antony will run in the Lupercalia race to demonstrate his athletic prowess.  Considered to be a man among men to the Romans, Antony fought in great battles, proving his bravery and courage.  He has been charged today with a special errand for Caesar.

Although Caesar would deny his beliefs in omens, he assigns Marc Antony to carry out one of the Lupercal's superstitions.

CAESAR (to Calpurnia)Stand you directly in Antonius' way, When he doth run his course. Antonius!
ANTONY                          
Caesar, my lord?
CAESAr
Forget not, in your speed, Antonius, To touch Calpurnia; for our elders say,
The barren touched in this holy chase, Shake off their sterile curse.

Calpurnia was to stand near the street.  As Antony passed by he is to touch Calpurnia so that she might become pregnant and bare Caesar a son.  Antony does complete this task as ordered by Caesar. Caesar wants a son with his legal wife to follow him as the ruler of Rome.

Of course, no such son is forth coming.  Caesar will be dead in a month, and Calpurnia is not pregnant.  Obviously, this superstition was prevented from completion possibly by the Soothsayer, who warns Caesar to beware the Ides of March.  Of course, Caesar pays no mind to this portent or forecast and goes into the nest of conspirators.

What is the relationship between Caesar and Calpurnia in "Julius Caesar"?

Caesar and Calpurnia appear to have a fairly conventional marriage by the standards of the Roman aristocracy. Caesar plays the dominant role in the relationship, as lord and master of all he surveys both at home and in the cutthroat world of Roman politics. For her part, Calpurnia is the dutiful wife: faithful, loyal, above suspicion, completely subordinate to her husband's wishes, and always willing to accommodate him in any way, shape, or form.

That said, she's not afraid to speak her mind if she feels that her husband's life is in danger. She doesn't hesitate to try and prevent Caesar from going to the Senate on the Ides of March after the many frightful omens that have taken place in the streets of Rome and all the terrible nightmares she's had. But this simply makes it all too easy for Caesar to patronize her, to treat her warnings as the products of a hysterical, overactive imagination. The archetypal macho Roman male Caesar will simply not allow his wife to exercise any influence over his actions.

We do not know how Julius Caesar and his wife Calpurnia interact when not under stress or in the public eye. What the audience sees suggests a strained relationship. She obediently replies, “Here, my lord,” when he calls for her at the fertility festival the Lupercal. Caesar states that “The barren, touched in this holy chase, / Shake off their sterile curse” when touched by the runner of the race. It is unknown whether Calpurnia’s inability to have children adds stress to their marriage and whether Caesar’s announcement of this embarrasses Calpurnia, but both are possibilities. When the race ends, Caesar grows angry and suspicious, and Brutus says that “Calpurnia's cheek is pale.” It appears that whatever hurts Caesar affects Calpurnia.

Later, Calpurnia has nightmares about Caesar’s death. This concerns Caesar, but he prefers to appear strong and dismiss his wife’s fears. Apparently not particularly superstitious or traditional, she says that she “never stood on ceremonies.” However, recent reports of supernatural occurrences frighten Calpurnia. Caesar argues with her, and she points out that his “wisdom is consumed in confidence.” He finally agrees to stay home, but only for her sake. Decius soon arrives and appeals to Caesar’s vanity and machismo, tempting him with the crown and suggesting that these prophecies are positive. Caesar believes what he wants to hear, rudely telling his wife, “How foolish do your fears seem now, Calpurnia! / I am ashamed I did yield to them.” Caesar will not succumb to a woman or to fear. His decision to ignore his adamant wife results in his death.