Should I ask the Editor for a third Referee when the answer of first two Referees do not agree? I submitted a theoretical paper to Physical Review Letters, and the editor answered that it can be published in Physical Review but it seems not suitable for a Letter given the Referee responses. 
Basically, one of the Referee recommends a Letter, while the other recommends a normal Physical Review. 

I would like to answer the editor/referee, in order to try to get published as a Letter. What is the best things to do in this situation? Of course, in any case, we should answer all the comments and try to convince the Referee. But is it useful to ask the editor for a third Referee in this case? Is it really hopeless to try to convince the Referee? Will be the third Referee a kind of a lottery?

More details about the specific situation:

One of the Referee praises our work for the interesting results, and for the clarity and readability of the manuscript. Also they say that it would stimulate new experiments, and recommend the publication as a Letter, after some minor points are addressed.

The other Referee however has a different opinion. They say that it is difficult to understand, cumbersome, and even raises a fundamental problem about our main result, which in their opinion is in contrast with the existing literature. Also, they say that the measure proposed will not stimulate the experimental community, since that, in their opinion, the measure seems not easy and there is no qualitative advantage in this proposal, compared with other methods.

Now, I and the other coauthors have fixed the manuscript, and we are able to show that our results do not contradict existing literature, and that the measure is possible (a very similar measure has been already done). I should remark that the topic of our manuscript is a phenomenon which has been confirmed very recently in 2 papers using the same experimental technique. Our proposal refers to a different signature of the same phenomenon. 

EDIT: I don't want to appeal, since I think that the Refereeing process has been fair, at least so far. Appealing should be reserved only in the case that one has the impression that the Refereeing was kind of unfair, biased, or fundamentally wrong.
The situation you are describing is not uncommon at all. Acceptance of an article in the prestigious Physical Review Letters is a big deal, and that is also the popular perception regarding it, primarily because of the high reviewing standards. Having personally attended a talk about this issue from one of the journal editors, I point out the technical correctness of work is not sufficient to guarantee publication in PRL - how much captivating is it for the Physics community is also a big factor. (Some part of this is hinted at, in the Acceptance Criteria of the journal.) Unless both the referees strongly recommend that the article qualifies to be a PRL on all eligibility counts, the decision is generally unfavorable. It is important to note that not all articles rejected by the journal are necessarily incorrect - some can rejected only because they were not deemed to be interesting enough!
In your situation, you can definitely appeal. This has been treated in the journal's Editorial Policies and Practices, under a separate tab of Appeals, from where I quote:

Authors may appeal a rejection of their paper by the editors. In the case of a formal appeal, the paper and all relevant information, including the identities of the referees, will be sent to a Divisional Associate Editor (DAE). The DAE may review the case on the existing record or may seek additional expert opinion. The DAE will present an advisory opinion to the editors, which will be sent to authors and/or referees with the DAE's name.
Authors may suggest those DAEs they feel are appropriate (or not appropriate) to conduct the review, but the editors are not bound by such suggestions. If there is no suitable DAE available, the editors may appoint an appropriate scientist to consider a paper under appeal as an ad hoc DAE.
The author of a paper that has been rejected subsequent to a DAE review may request that the case be reviewed by the Editor in Chief of the American Physical Society. This request should be addressed to the Editors, who will review the file and, if appropriate, forward the entire file to the Editor in Chief. Such appeals must be based on the fairness of the procedures followed, and must not be a request for another scientific review. The questions to be answered in this review are: Were our procedures followed appropriately and did the paper receive a fair hearing? A decision by the Editor in Chief is the final level of review.

Please note that the above form of appeal is more of a fairness measure from the point of view of the journal - just in case the authors feel they haven't got a fair review. You must note that the official statement here is &quot;In the case of a formal appeal, the paper and all relevant information, including the identities of the referees, will be sent to a DAE&quot;. So, the report by the second referee (as well as info as to who this guy is) shall also be sent to the DAE. Thus, he can also uphold the second referee's verdict if he considers it appropriate, i.e. if the reasons appear genuine. But, of course, he may also rule otherwise.
Quite obviously, this appealing does not guarantee that the paper makes the cut in the journal, it is only like a half shot more at it. It may also happen that the DAE may not feel that it makes a very strong case for a letter, even though there may not be any fundamental flaw with the results. If that happens, and even otherwise, don't feel very bad about missing out on a PRL. It is much more important that the contents of the article are correct, and the Rapid Communications section of Physical Review A/B/C/D/E might be a safe bet too. And of course, you can always opt for other letter journals. But if you think it makes a strong case, PRL does offer you a procedure for appealing too. Avail it if you wish.