To be frank, you would be incredibly foolish to go through with the wedding if she doesn't sign.

Consider seeing marriage as a business contract. Why would you take such a risk, especially considering how you've been burned once before? Especially considering now that your kids will also potentially suffer the collateral damage?

Also, I call bs on her excuse that it's a barrier to your relationship. There is no logical reason why it should be if she truly intends to marry you for life.

If she's being this unreasonable now, imagine what it will be like when the honeymoon phase is over when you as a couple have to phase challenges together.

This is a huge red flag, and I think deep down inside you know it.