I suppose there are many examples of characters being forced to face reality throughout Romeo and Juliet, but my favorites is the scene between Romeo and Juliet that takes place in Act 3, scene v after they have shared the marriage bed and Romeo knows that day is breaking and he must leave, but Juliet begs him to stay.
Romeo And Juliet : Act 3, scene v, 11-13, 16, 17-27, 30-36
ROMEO I must be gone and live, or stay and die.
JULIET Yon light is not daylight, I know it, I.
It is some meteor that the sun exhales...
Therefore stay yet. Thou need'st not to be gone.

ROMEO Let me be ta'en. Let me be put to death.
I am content, so thou wilt have it so.
I'll say yon grey is not the morning's eye.
20'Tis but the pale reflex of Cynthia's brow.
Nor that is not the lark, whose notes do beat
The vaulty heaven so high above our heads.
I have more care to stay than will to go.
Come, death, and welcome! Juliet wills it so.—
25 How is 't, my soul? Let's talk. It is not day.

JULIET It is, it is. Hie hence! Be gone, away!
It is the lark that sings so out of tune,...
30 This doth not so, for she divideth us.
Some say the lark and loathèd toad change eyes.
Oh, now I would they had changed voices too,
Since arm from arm that voice doth us affray,
Hunting thee hence with hunt's-up to the day.
35 O, now be gone.More light and light it grows.
ROMEO More light and light, more dark and dark our woes!

Janeyb's answer is correct, though I would add that Romeo Montague is her family's longtime nemeis, not Juliet's own.

Following up on this idea, reality also strikes hard for both the Capulet's and Montague's following the tragic deaths of both of the children. They realize in 5.3.304-311:

CAPULET O brother Montague, give me thy hand:
This is my daughter's jointure, for no more 305
Can I demand.
MONTAGUE But I can give thee more
For I will raise her statue in pure gold;
That while Verona by that name is known,
There shall no figure at such rate be set
As that of true and faithful Juliet. 310
CAPULET As rich shall Romeo's by his lady's lie;
Poor sacrifices of our enmity!

Although Romeo and Juliet often avoid reality by secluding themselves, sometimes reality hits them, and they cannot avoid it, the following passage is a situation in which Juliet cannot avoid the fact that Romeo is her families sworn enemy.

My only love sprung from my only hate!
Too early seen unknown, and known too late!
Prodigious birth of love it is to me,
That I must love a loathed enemy (I, v)

After falling madly in love with her mystery man, Juliet must face the reality that he is, in fact, her enemy.