How do I prove that Friar Lawrence's potion is not the best soution for Juliet's dilemma?

Perhaps the best way to make this argument is by looking at the events that actually transpired after Juliet drank the potion. The potion itself actually worked--it did what the Friar promised it would. But all depended on getting news of the plot to Romeo, who was banished to Mantua. Friar John, as it turns out, was unable to get to Mantua due to plague, but Balthasar, Romeo's servant somehow got through to tell Romeo that Juliet was dead. Perhaps Friar Laurence should have anticipated that Romeo might receive reports of Juliet's "death" instead of learning the finer points of the plan.

In other words, the Friar's rather ill-conceived plot was very dangerous, and that many things had to go right for it to work. It is also important to remember, however, that the Friar really had little choice--Juliet has already warned him that she will kill herself rather than marry Paris. "I long to die," she says, "if what thou speak'st speak not of remedy." Perhaps, then, the safest (but certainly still dangerous) choice might have been to smuggle Juliet out of Verona to Romeo. But that, possibly, would not have achieved the Friar's motive of reconciling the two families--indeed, it may have made things worse.