What happens if someone will not sign a 2 year conditional visa?

If you get a divorce, you can file an I-751 waiver.

If you are married, you have to have your spouse sign the paper to remove the condition on your permanent residence. The alternative is to get divorced, and then request a waiver of spouse's signature. Or if spouse abused you, you can apply as an abused spouse. If you don't file anything before the green card expiration date, you might be put into removal proceedings. Please seek attorney's help at your earliest.

If your wife is not cooperating on the I-751 removal of conditions, and you are divorced; you can file the I-751 on your own requesting a waiver of the joint filing requirement based on a "good faith" marriage. Show that you have a child together, cohabitation and co-mingling of funds and you should be approved.

There are 4 ways to get the removal of the condition done. Here they are from the easiest to the most difficult: 1. Live together with your spouse + get along. The American citizen signs the paper together the Alien spouse. Provide proof you got married in good faith. 2. File for divorce. Only you sign the form. Explain why the relationship is not working. Provide proof you already filed for divorce. Provide proof you married for the right reasons (joint documents). Later, the USCIS will ask for your final judgment of dissolution. 3. Domestic abuse. Must show you were abused. Must also show you got married for the right reason. (No need to file for divorce). 4. Hardship. Must explain your hardship and all the bad things that will happen if your removal of the condition is denied. Document it well. (I personally used this one only once). Good luck.

If she refuses to sign I-751,petition to remove condition, you should file divorce and then file I-751 yourself based on good faith marriage exception to file joint petition. If you can show the marriage is bona fide, CIS would still approve your petition.