First, regarding the exemptions for the kids. It is very unusual in a divorce for one parent to take all of the exemptions. Usually they are split or the parents alternate every other year. Also, the child tax credit of $1,000 only applies to kids 16 or under at the end of the year (2010).
If you claim all of the kids, then your taxable income for 2010 will be around $25000 and the tax on that is $3331.
If you take out $10,000 from the ESP, your tax goes up to $5000. If you take $20,000, the tax goes up to $7,500.
So, if you have 3 kids 16 or under that you claim, you will have credits of:
Child tax credit 3,000
American Opportunity Credit 2,500
Federal tax withheld 2,093
Total credit 7,593
These amounts also assume you have itemized deductions of $13,000. This includes mortgage interest, state taxes paid in, real estate tax, and charity. Please let me know if this number is XXXXX close to your actual expenses.
To address the filing status issue, you may file as Head of Household, however this only matters if you are taking the standard deduction (vs. itemizing).
Regarding your W-4 status of single/3, this is for your employer to calculate your taxes and does not obligate you to that on your Form 1040.
To sum it up, if my assumptions are in the ball park, you will not owe any additional taxes (federal) on April 15 even if you take the $20,000 from the ESP. If not, let me know what you want me to change and I will recalculate.