Should I take a new job and underestimate the amount of taxes that would be taken out of my signing bonus to my wife?
Are you serious? Why do you plan on misrepresenting your tax burden to your wife?
I don't want her to know how much money I'm getting.
Misrepresenting the amount of taxes that are going to be taken out of your signing bonus to your wife is wrong, because married couples are supposed to be honest with each other regarding financial information. I think you should tell your wife the truth about your signing bonus because you want her to trust you.
The amount of money I'm giving her is hers anyway. She should have no say in the matter.
What if she finds out later on that you have been lying about your finances? It is just a matter of time before she will think you are untrustworthy and might even question your overall character. Is it really worth it to lie about your finances?