Modal Verbs – Should in Conditional Sentences

A conditional sentence has two parts: the "if-part", or protasis, and "then-part", or apodosis.

In the apodosis, we use would to create that "conditional" feeling. So the sentence

If we had had lots of money, we should have travelled round the world.

would be illogical: the protasis clearly says that we did not have money during some period in the past, but the second half of the sentence is not an apodosis, because it uses the wrong modal verb. The second half looks like a normal sentence on its own:

We should have traveled around the world! (instead of doing some other things in the past, we should have traveled around the world)

This clause implies that we had the ability to travel around the world. It contradicts the protasis.

The same applies to your conditional 2 example:

If I worked harder, I should pass the exam. [improbable situation in the present or future],[moral obligation]

The first part invites some apodosis with would. The second part just plainly states your obligation to pass the exam. But according to Wikipedia,

Occasionally, with a first person subject, the auxiliary would is replaced by should (similarly to the way will is replaced by shall). (Wikipedia says this about the apodosis of both the second and the third conditional)

So maybe we can use should there after all, since I is a first-person subject. Let a native speaker decide.

The use of should is usually "deontic" (what should be: used to express norms, expectations, speaker's desire) while the use of would is "epistemic" (what may be).

The modal verb should could be sometimes used in the epistemic mood too, so we can come up with sentences such as

If I worked harder, that should be surprising!

But the effect would be comical and ironical, not the usual effect with the conditional sentences. The two halves of the sentence would still look somewhat disjointed.

I'll try and do my best to answer this question, in such a way that you'll be able to make some sense out of this, and then apply these guidelines in the future.

The first sentence is an example of the so-called second conditional

If you were a king, what'd your wife be called?

Rightly so, edyta—the OP—said this is an impossible situation. The chances of edyta, whom I presume is a woman, becoming king is even more remote. But the sentence doesn't refer to a past event. Being a king never happened and it never will. The idiomatic phrase If + you + were is expressing an unreal situation, similar to saying: Let's pretend you are a king.

The construction If + subject + past and would + infinitive is often referred to as irrealis, which means that the situation proposed is ‘unreal’ or ‘imaginary’ in the present
_{See also Present Unreal Conditional}

The past verb-form is used to suggest that the situation is probable, or imaginary, or set in a hypothetical future.

Martin Parrott provides this insight:

We use them [type 2 conditional sentences] to refer to or speculate about something that is (or that we perceive to be) impossible or ‘contrary to fact’. This is sometimes presented to learners as ‘very unlikely’. The real point, however, is that at the moment of speaking we see the action or event as being impossible.

^{Source: Grammar for English Language Teachers}

• Probable; e.g. “If I were on holiday, I'd go to the beach every day.”

• Imaginary; e.g. “If I were a cat, I'd catch mice all day long.”

• Or hypothetical future event; e.g. “If I had a car, we would drive down to Mexico.”

The OP's example falls under the category of imaginary, If I were a King. . .

The following sentence is an example of a hypothetical future event

A: What would you do if you needed a haircut?

i. I'd go to the hairdresser's.
ii. I'd cut it myself.
iii. I don't know. Cut it, I guess. Why are you asking?

The so-called ‘third conditional’ is for talking about a hypothetical/imaginary situation in the past (which didn't happen) and its consequence.

If you had worked harder last year, you would have passed your exam
if + past perfect and would have + past participle
_{See also: Past Unreal Conditional}

Thus the sentence (note my correction on the word order)

If you had been king, what would your wife have been called?

Expresses either an imaginary situation in the past that didn't happen, or an event that didn't happen in the past. In both cases, the situation is ‘impossible’ because we cannot change the past.