If you owe taxes for previous year - you may not "make up" the difference by increasing withholding for the current year on W-4 and IT-2104 forms.
past due tax liability and withholding for the current year - should be addressed separately.
For your past due taxes - you need to amend your federal and state income tax returns and determine the exact amount of tax liability.
You will also owe late payment penalties and interest based on the amount of additional tax liability.
If you can't pay - you need to contact IRS and NY Department of Taxation and Finance and set an installment plan.
For your withholding filing - as you both - you and your wife - work - you may check -
"Married, but withhold at higher Single rate"
You will claim
1 allowance for your self
1 - because nobody claims you as a dependent
2 - for your child (1 for dependent and 1 - for child tax credit if your child is below 17) - be sure that only you or only your wife claim allowances for the child.
as you own a home - you will likely itemize - if so - add one allowance for each $3,650 above the standard deduction - please also be sure that only you or only your wife claim these allowances - but not both.
see for reference
If you need help to estimate your total tax liability - we would need your total income for the year and the amount of itemized deduction.
Let me know if you need any help.