Correct, all you have to do is make a payment under your spouse's SSN. If you want to mail a check, you can use the tear-off voucher on the last page of form 1040-ES. If you make the payment online, be sure to select that it is for third quarter 2016 1040-ES.
At this stage the IRS only wants their money. There are various forms and methods of calculating the estimated payment needed, but all of that is just an estimated. Your tax return that you will prepare in March or April will list all your income, all your deductions, calculate your tax, account for all your withholding and payments, and tell you if you owe more or get a refund. That will be the definitive word on what you owe for the year.
