How do Protestants explain Zechariah 12:10-14, used by Roman Catholics to prove Mary's perpetual virginity?

First of all, we need to look at the context of the passage. More specifically the kind of genre. Zechariah is prophetic literature which is filled with symbolism, metaphors and simile to describe future events. Zechariah specifically - [as opposed to say Isaiah who writes many prophecies about the first advent of the Messiah] is writing about the second advent of the Messiah. Zechariah writes about end times events, the terrible Day of the Lord or Second Coming when the sun turns black and the moon to blood. No one thinks the moon literally changes into blood . Rather, he is describing a blood moon - which has for millennia been an omen to Jews. So the context within the book is not pointing to or describing events at the Birth of Christ, but his return after the Tribulation. Secondly, he is using figurative language. It is a very weak argument because he's not referring to Mary, or Joseph or the birth of Christ. The other thing is that the second passage you mention in Luke 2 mentions "a sword will pierce your soutsl" referring to Mary, but we know this is hyperbole or symbolism for the pain Mary would later feel at the death of her son. Protestants take this and all other prophetic passages and interpret them in light of clear passages and eyewitness accounts which say that Joseph did not sleep with Mary until after Jesus was born.
One principle of Biblical interpretation and a quote from Bible scholar and professor Dr Alan Brown- "If at first the text seems to make literal sense- seek no other sense or it will be nonsense".

The interpretation varies among Protestants, but most do not believe Zechariah 12:10-14 is at all in reference to Mary or the first advent of Christ. If read in full, it can be seen the verse is not related to the mourning at the time of Jesus death and burial, but a future mourning that will occur when the Jewish people as a nation come to faith in Christ. There is no evidence of a historical fulfillment of the passage as a whole. The nation of Israel and their tribes did not mourn the loss of the Jesus in the way this passage describes. Read on:

12 And the land shall mourn, every family apart; the family of the house of David apart, and their wives apart; the family of the house of Nathan apart, and their wives apart;

13 The family of the house of Levi apart, and their wives apart; the family of Shimei apart, and their wives apart;

14 All the families that remain, every family apart, and their wives apart.

This is yet to transpire. This verse points towards a future period of time when Israel will come to faith in Christ. It does not point to Mary.

And I will pour upon the house of David, (Why does he mention the house of David? Because this is a part of the Judean tribe and he was a king that brought Israel together, the only one that ever brought the whole house of Israel together. It stayed together under Solomon, but Solomon began to be a rigorous king. He began to burden Israel with taxation because he began to build. Just like the government is doing now. Did you notice all the construction in the last few months? It is election time. After the election, then it will stop and the roads will be bad again. Solomon began to marry all these wives. For his Egyptian wife he built a great palace. By the time he was through, God was through.) and upon the inhabitants of Jerusalem, (Jerusalem is the place of David. Jerusalem has a revival coming. That is where the two prophets will be.) the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn. In that day shall there be a great mourning in Jerusalem, as the mourning of Hadadrimmon in the valley of Megiddon. And the land shall mourn, (The land shall mourn, that means the nation.) every family apart; the family of the house of David apart, and their wives apart; the family of the house of Nathan apart, and their wives apart. The family of the house of Levi apart, and their wives apart; the family of Shimei apart; and their wives apart; all the families that remain, every family apart, and their wives apart. See, there is a great mourning. Why? Because of Zechariah 12:10. Jesus appears there, they seem him, and they realize the truth at that time. -The Contender magazine

The Protestant view of Zechariah 12:10 :

And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and of supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn. [KJV]

is ably expressed by John Gill (1697-1771), a Strict Baptist pastor and scholar, see Wikipedia :

and they shall mourn for him as one mourneth for his only son; or, "for this"; that is, piercing him; for sin committed against him; because of their rejection of him, their hardness of heart, and unbelief with respect to him; and on account of their many sins, which were the occasion of his being pierced; which mourning will arise from, and be increased by, a spiritual sight of him, a sense of his love to them, and a view of benefits by him. Evangelical repentance springs from faith, and is accompanied with it; and this godly sorrow is like that which is expressed for an only son; see Amos 8:10 and indeed Christ is the only begotten of the Father, as well as the firstborn among many brethren, as follows:

StudyLight (Extract of the John Gill's Coomentary of the Whole Bible)

Here, John Gill takes the prophecy as applying the mourning not to natural Israel but to the true Israel of God, namely those born of the Spirit in a new birth, for 'they are not all Israel who are of Israel' Romans 9:6, but they are true Israelites who have believed on the Son of God.

And John Gill applies the reference to 'only son' and 'firstborn' spiritually, not naturally, to the Deity of Christ, namely to his being the only begotten of the Father, John 1:18, and to his being the firstborn of every creature, Colossians 1:15.

This Protestant treatment of the verse applies the words spiritually, to those who believe in Christ and who mourn for him in respect of their own sins having pierced him - not with respect to nails through flesh and bone, but with respect to the judgment of God upon him at Golgotha, his sufferings being the offering of himself, the Son of God, in humanity as the Sin Bearer on behalf of many.

The idea of Mary espousing herself to Joseph whilst avowing to remain a virgin is answered in other answers on the website, the Protestant view being that the four gospel accounts make it clear that after the birth of Jesus the marriage of Joseph and Mary brought forth a number of siblings.

In @curiousdanni 's answer the point is made that the overall weakness of the argument that Mary remained a virgin after Jesus' birth is highlighted by the attempt to trivialize such a spiritual prophecy as Zechariah 12:10 in order to try to construct an argument from it that scripture, as a whole, simply does not support.

This is a very weak argument for the perpetual virginity of Mary. This verse uses a simile to say that Israel's mourning for their God-Messiah will be like that of parents who have lost their only child. It makes no claim whatsoever about Mary. The proposed argument takes a figurative use of language about one subject (the weeping of Israel collectively and nationally) and applies it literally to a different subject (the singular woman Mary). And so even if you did want to use this image and apply it to Jesus literally, then the most justifiable parallel would be the mourning of Israel over their only Messianic Son of David, or perhaps, as representatives of Israel, the mourning of his disciples.