How were obstacles between Beatrice and Benedick overcome and true love preserved in Shakespeare's Much Ado About Nothing ?
After Beatrice and Benedick are tricked into falling in love with each other, their love faces an obstacle when Claudio publicly disgraces Hero. Beatrice wants to avenge her beloved cousin and demands of her new love Benedick, "Kill Claudio" (IV.i.297). When Benedick refuses, Beatrice decides that Benedick's love for her is actually false and that he is incapable of loving, as we see in her lines, "There is no love in you" (302-303). However, Benedick refuses at first for a couple of reasons. The first reason is that he realizes that Claudio and Don Pedro, both honorable men, have been tricked somehow by the dishonorable Don John. We see this when the friar reasons that the princes have somehow been misled and Benedick concludes:
Two of them have the very bent of honour;
And if their wisdoms be misled in this,
The practice of it lives in Don John the bastard,
Whose spirits toil in frame of villainies. (194-197)
The second reason why he cannot bring himself to fulfill Beatrice's request is that he very much loves Claudio who has become his very dear friend. However, Beatrice finally persuades Benedick that Claudio has "slandered, scorned," and "dishonoured" her cousin; therefore, Benedick goes off to challenge his dear friend Claudio (311).
Benedick and Beatrice overcome this obstacle when Claudio's guilt is cleared. It is proven that Don John perpetrated a fraud to trick both Claudio and Don Pedro into slandering Hero, and Claudio is overcome with the deepest remorse. Claudio is asked to marry Leonato's niece but in actuality he marries Hero. The union between Claudio and Hero serves as a means of overcoming Beatrice's and Benedick's obstacle because now that there is no longer any reason for Benedick to kill his dear friend Claudio, the couple can safely be united, preserving their true love.
In this play of Shakespeare it is not so much how true love conquers obstacles but Shakespeare's major theme of appearances vs. Reality and social expectations, in his tragedy's such as Macbeth we see how deception can have devastating results, but in this comedy, he simply alludes to the potential tragedy that lies in the antics of those who, apart from Don John, have good intentions.
But in answer to your question, love brings together characters, Beatrice and Benedick, character's who themselves have said they will never marry. They are both strong characters, witty and independent, love creates a situation in which they no longer have to be alone. Their love also shows some deep realisations for both characters about the ideals they have so far lived under. Both are quite unaware of how sharp their wit is and the adverse effects it can have on those to whom it is directed. But together they seem to moderate each other a bit and become more aware of what they say. Their love has shown a development of their characters. Shakespeare alludes to the fact they had a relationship in the past which was ended due to Benedicks antics, and clearly Beatrice has not forgiven him, while Benedick obviously does not see it as his problem. Both hide behind their quick wit, showing beneath the surface they are both very sensitive. Beatrice is actually a very venerable character as is Benedick, and when their love develops they embrace it as this venerability can no longer be seen as a weakness but an endearing trait. So essentially love brings out a truth in their characters, an acceptance of their lives and the fact happinness can actually be found from love and it is not weak to admit it.
For Hero and Claudio (Claudio being a much weaker character in comparison) their love perhaps cannot be considered as true love. Claudio asks Leonnato if Hero is his only heir, alluding to his potential desire for significant economic gain from a marriage. And when Margaret is mistaken for Hero, Claudio does not seek an explanation or confrontation with Hero immediately, instead choosing to publicly humiliate her. He is ruled by his quick to fire feelings as opposed to the rationality someone like Beatrice has which allows her to give Hero the benefit of doubt. Claudio perhaps is more interested in the idea of love as opposed to love itself of which he is rather naive. Hero is simply a delightful young woman, polite, generous and loyal. Her innocence is her most endearing quality, one which Claudio very nearly destroys, but their love does succeed in the end, showing true love promotes forgiveness.