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Is it correct to write the following sample sentence?

"I would go with you if you would pay for my movie ticket."

Does the sentence contain two conditional clauses? In what other situations, besides the example, can you use this kind of sentence?

If you are to replace "would" by "should", would the sentence make sense because I learnt that "should" is the conditional form of "shall", just like "would" is the conditional form of "will"? "I should go with you if you should pay for my movie ticket."
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I'd write:
"I would go with you if you paid for my movie ticket"

"I would go with you" doesn't express a condition, but it uses the conditional tense; it expresses an eventuality.
The conditional clause begins with "if..."
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Is it correct to write the following sample sentence?

"I would go with you if you would pay for my movie ticket."

JTT: Yes, it's fine, Procrastinator. Here, 'if you would' is the volitional 'would', it's questioning the person's willingness to shell out for the ticket.

"I would go with you if you would [be so kind as to] pay for my movie ticket."

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Does the sentence contain two conditional clauses?
If you are to replace "would" by "should", would the sentence make sense because I learnt that "should" is the conditional form of "shall", just like "would" is the conditional form of "will"? "I should go with you if you should pay for my movie ticket."

JTT: You were mislead by whoever taught you this. All the modals are used in conditional sentences but they are not conditionals in and of themselves. There is no need to replace 'would' with 'should' though it's certainly possible.

'would' assumes a certainty, a 100% chance that the person is willing to pay for the ticket. 'should' weakens it slightly ['should' equates to 'probably']. Using 'will' or 'would' with 'if' makes it almost like a question, it questions the person's willingness to pay for the ticket.

'will' has the same meaning, 'would' is only more polite, more deferential because of its greater remote nature.

"I would go with you if you will pay for my movie ticket."

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Procras wrote:
In what other situations, besides the example, can you use this kind of sentence?

JTT: ENLs also use 'would' in some situations to add a more emotive feeling to some 'if' conditionals, both present and past.

If he wouldn't + present tense ----, S would ------ .

If she wouldn't have + PP ----, S would -------- .

Put "if they wouldn't" [you can use other pronouns like 'she/he'] into an exact word Google search and you can see how this structure is used.
Students: We have free audio pronunciation exercises.
Comments  
So it's not possible in English to say "...would...if...would..." ?
 just the truth's reply was promoted to an answer.
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