Your example is a mixed conditional, where the cause (signing the paper) is in the past, and the consequence (the problem) is in the present. You may want to read my mini-article. Grammar boost: Conditionals cheat sheet PART 1: https://www.italki.com/discussion/164505

Your sentence would be better said like this: If you hadn't signed this paper, we wouldn't be having such a problem now.

The second conditional is for an unexpected/impossible hypothetical present or future and the hypothetical consequence. - If it snowed tomorrow, the schools would close, and I would have to stay home with the children. alternate (If it were to snow tomorrow, the schools would close, and I would have to stay home with the children.) The third conditional is for a hypothetical past and a hypothetical consequence. It is sometimes used to reproach people. - If it had snowed yesterday, the schools would have closed, and I would have had to stay home with the children. - If the hurricane had landed 100 kilometres to the south, it would have hit Miami and (it would have) caused major damage. - If the hurricane hadn't landed in a mostly rural area, it would have caused major damage. - If you had studied more, you would have passed your exam/you wouldn't have failed your exam. (reproach) - If you hadn't partied so much, you would have passed your exam/you wouldn't have failed your exam. (reproach)

You have signed the paper (in past) and we have problems (now). The rule says: in this situation you should use second conditional (past + would present). So I'm trying: "if you hadn't" ... stop wait it turns into a third conditional now! What should I do? Those are the thoughts came to my mind.

Yes, 'hadn't' means it's 3rd conditional - in the past. Can you describe the situation? Is the 'signing' not in the past? Why do you want to use present perfect if it's not in the past??