Taking the children on both W4's may result in not having enough withheld. You can plan to have additional withholding to cover her contract income, or you can make estimated tax payments.
The IRS has a W4 calculator that can be helpful with these situations. Start by going through these screens.
Your wife can claim 0 dependents and if needed have additional funds withheld. You want to be sure that you pay enough in so that you do not end up with more than $1000 not withheld.
A penalty is imposed if there is more than $1000 underpaid.
