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.
Best Answer
You must relocate the time-phrase to clear up the ambiguity.
It came out last winter that she was already married.