Learn English – This is going to be the chance to [verb] any difficulties. Solve or sort out

"Dance it out" is not, to the best of my knowledge, a common phrase. The writer likely invented the phrase here.

There IS a common idiom, "work it out", meaning, to solve a problem by applying sufficient effort. I think the writer here is playing on that idiom to say that a person can solve his problem by dancing. That is, instead of "working [the problem] out", he will "dance [the problem] out". The problem here is stress, so the statement is not irrational. It seems plausible to say that one could overcome stress by dancing or some other energetic but fun activity.

In contexts like these with has two unrelated uses.

• We use a with phrase after verbs like talk, discuss, argue, talk over, take up, sort out to designate the other people involved in the activity: the people we are addressing. The with phrase modifies the predicate—the verb and its complements—and ordinarily comes after the predicate is 'finished',

  ...an issue ... to sort out with the labor boards
  ...an issue ... to take up with their legislators
  ...a problem ... to discuss with my boss

• We also use a with phrase with nouns like problem, issue, difficulty to designate the location of the problem: where the problem arises. The with phrase modifies the noun and ordinarily comes immediately after it.

  a problem with fraud ...
  a difficulty with English idiom ...
  an issue with his attitude ...

Both of these uses are idiomatic. But (as I suspect you have realized) a problem may arise when your utterance involves both a noun and a verb which may each take a with phrase. There are two sorts of problem here:

• The first is ambiguity:

  We need to discuss this problem with the labour board.

  Is the labour board the source of your problem or the agency you want to discuss it with?

  In conversation the ambiguity will usually not arise: the context and the situation will make it clear to your hearer which you mean, and any misunderstanding will eventually emerge in the conversation and can be explained. But in writing you have to deal with the fundamental rule that “Anything which can be misunderstood will be”; since you have no opportunity to clear up any misunderstanding you must take particular care to say exactly what you mean.

  I’ll address some rewriting strategies shortly; but one that jumps forward in your example can be addressed here. With some ‘phrasal verbs’—sort out is one of them—the second element is separable—it can be placed either before or after the Direct Object. However, it should not be placed after a ‘heavy’ (many-word) DO, and it should not interrupt a DO. In your example the with phrase modifies this problem and should not be separated from it. Putting out after this problem leads the reader to believe that this problem is the entire DO, so the with phrase must be a modifier on the predicate: the person with whom you will sort out the problem. That is obviously absurd in this context, so there’s no real harm done; but out really should come before this problem:

  I have to sort out this problem with the fraud involving my credit card.

  That ‘ties’ the with phrase to the problem and makes misunderstanding much less likely.

• The second problem is horror aequi: our strong dislike for using the same construction twice in a row with different significance:

  We need to discuss this problem with the labour board with our lawyers.

  Here there’s no permanent ambiguity, even in writing: when readers get to the end of the sentence they will apply the ‘rule’ that the first with phrase modifies the NP labour board which immediately precedes it, so the second with phrase modifies the predicate-as-a-whole.

  But the sentence is likely cause a brief ‘glitch’ in interpretation—after all, it is not unreasonable for readers to suppose, when they encounter with the labour board, that you feel a need to discuss your problem with the people who are causing it. And then you add a second with phrase with a different meaning, and that makes readers re-calibrate their interpretation of what the with signals—that’s probably why we dislike these doublings. So by the end of the sentence your readers may feel a vague sense that you have made your sentence unnecessarily difficult to follow.

  In conversation this is not a severe problem: you have all the resources of intonation and phrasing to make your meaning clear, and can speak your sentence something like this:

  We need to discuss this  problem-with-the-labour-board   with our lawyers.

  But you can’t do that in writing.^† You really need to rewrite. You have a lot of options. For instance, very old-fashioned writers will flip the Direct Object and its modifying with phrase to the end:

  We need to discuss with our lawyers this problem with the labour board.

  There’s enough separation between the with phrases here to overcome horror aequi. But the separation between the verb and its Direct Object is unnatural and ‘literary’; in modern prose this should be avoided. Another approach would be to separate the two with phrases through an ‘information packaging’ strategy like passivization or extraposition:

  This problem with the labour board needs to be discussed with our lawyers.
  This problem with the labour board, we need to discuss it with our lawyers.

  An even better solution is provided in TRomano’s answer: recast one of the with phrases.

  We need to discuss this labour board problem with our lawyers.

^† _{Well, you can—I just did—but that’s going to make your page look very odd, and will be even more annoying than horror aequi.}