A hypothetical scenario: Lets assume that Tybalt didn't attack Romeo, Mercucio didn't die, Romeo didn't kill Tybalt and as a result he wasn't banished. Lets say that the secret relationship between Romeo and Juliet then goes on for a little longer than presented in the play (before they get married), and that they haven't had a physical relationship. After a little while, they realize that if they don't act, then eventually the cat will get out of the bag, causing renewed tensions between their two families. To make matters worse, the longer they stay unmarried, the more likely they were to be separated through circumstances beyond their control, or through their families finding out. Since their feelings are growing stronger to each other, they would have to either get married soon, or break the relationship off. The two decide to get married, with Father Lawrence's help, as per the story. Father Lawrence sees it as a perfect opportunity to end the feud between both houses peacefully, and so agrees to help them, but on one condition that the ceremony is a public wedding. This means that Romeo has to approach Sir Capulet and not only declare his love for Juliet, but also ask his father's most hated enemy for her hand in marriage. Now, before you say that it would not end well, keep in mind the following about Lord Capulet: 1. It is clear that Lord Capulet has a grudging respect for the boy, based on his commentary and chastisement to Tybalt during the party (though that also may have been just to avoid crashing the party). Although he hates Romeo because he is a Montague, Lord Capulet clearly admits that from what he has heard, that Romeo is a respectful, honorable, and honest boy. 2. He won't risk hurting Romeo because the Prince of Verona recently began cracking down on the feud between the two houses, and if he did, word would certainly get out, and he would get in serious trouble. 3. If his head is clear, He could see the advantage in ending the feud between the two families through this marriage... though at the very least he would probably think it as some Montague trick. 4. Both The Nurse and Father Lawrence are relatively neutral parties that could provide testimony that Romeo's intentions are honest. They can easily testify that that Romeo truly does love Juliet, and that she does love him. 5. Juliet can personally confirm that she does love Romeo, and is not only willing to take his hand in marriage, but eager to. 6. If Romeo & Juliet can get along, then surely their parents would soon realize that their families can get along as well. 7. The cause of the feud was forgotten long ago. 8. We can assume that Montague would also come to similar conclusions above. Again, lets assume that both family patriarchs are acting somewhat rational with this. Some outrage is to be expected, but once they've calmed down, maybe their minds will realize that this impromptu arranged marriage is a good thing. Q: What would happen in this situation, given both the best case and worse case scenario? How would Sir Montague react, and how would Sir Capulet react in Romeo and Juliet? [Disclaimer: This is a question asked out of curiosity.]

With the conditions mentioned above, there could be a resolving of the conflict between the two families provided the Lords Capulet and Montague were agreeable to the union of Romeo and Juliet.
While Lord Capulet does not seem to be the initiator of conflict, he is not one to shy from it. In Act I, for instance, Capulet angrily calls for his sword as Montague "flourishes his blade" (1.1.68). For this reason, it would seem, then, that the initiator of amelioration should be Lord Montague, yet Montague is angered when he sees Capulet and is ready to fight; furthermore, he is held back only by Lady Montague.
Lord and Lady Montague love their son dearly, for they are deeply concerned about his melancholy state. Similarly, the Capulets love their daughter as evinced in the protective Lord Capulet's reluctance to speak to Count Paris of his daughter's marrying him:

My child is yet a stranger in the world--She hath not seen the change of fourteen years.Let two more summers wither in their prideEre we may think her ripe to be a bride. (1.2.8-10)

In fact, it is this protectiveness which acts as a deterrent to the possibility of young Juliet's marrying Romeo more, perhaps, than the feud. For, when Lord Capulet does decide that Juliet should marry, the marriage is determined by him. He informs Juliet that she will marry Count Paris. But, when Juliet demurs, Lord Capulet becomes angry, just as he does when Tybalt wants to kill Romeo.With Lord Capulet as a rather domineering patriarch, it seems doubtful that he would approve of Juliet's marriage to Romeo, despite his appreciation of the young man's character. Nor is he influenced by his wife, who is merely submissive to his orders; for, she will not listen to Juliet even as her daughter threatens to kill herself if she is made to marry Paris.
In addition, while Lord Capulet does recognize the sterling qualities of Romeo at the celebration for Juliet, he forbids Tybalt from doing anything because he does not wish to upset his guests. Therefore, it seems that he wishes to be the one who controls events. When Lord Capulet is not in control, conflict seems to follow.
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Much less is known about Lord Montague than there is about Lord Capulet since he appears only in the beginning of the play and in the final scene. In both instances, Lord Montague demonstrates his love for his son. In Act I, for instance, he is concerned that Romeo has not shown himself and appears gloomy over a woman. Lady Montague asks Benvolio if he has seen anyone because they are worried about their son.Lord Montague complains that Romeo keeps too much to himself. So, he would clearly prefer to interact with his son and might be open to Romeo's marriage to Juliet if he felt that Romeo truly loves the girl. However, this is mere conjecture as Montague does harbor hatred for the Capulets.