You are the higher wage earner. So you claim both of your children. (assuming he is the father of those children)
He files single and gets the $6,400 standard deduction just for breathing, and his $4100 self-exemption. That totals $10,500 which means he will pay no taxes at all for 2017.
You also file single. You get the $6,400 standard deduction just for breathing, the $4,100 self-exemption, plus another $4,100 for each of your children. That totals. $18,700. Subtract that from 35K and you'll be paying taxes on $16,300 of your earned income.
If you qualify to claim Head of Household, then your standard deduction will be $9,350 meaning you'll only pay taxes on $13,350 of your income.
Of course, your actual taxable income may be lower depending on what other deductible expenses you may have, such as job related expenses, teacher expenses (if you're a teacher), mortgage interest, student loan interest and the such.
